diff --git a/.github/workflows/cron-tests.yml b/.github/workflows/cron-tests.yml
index 2cf155cba..e22b45243 100644
--- a/.github/workflows/cron-tests.yml
+++ b/.github/workflows/cron-tests.yml
@@ -19,12 +19,12 @@ jobs:
       fail-fast: true
       matrix:
         os: [ubuntu-latest, macos-latest] # TODO: re-enable windows-latest
-        python: [3.7, 3.8, 3.9]
+        python: ['3.8', '3.9', '3.10']
         include:
           # These set options for each python version. So, for example, when any
-          # python 3.7 job in the matrix runs, it should use this toxenv
-          - python: 3.7
-            toxenv: py37-test
+          # python 3.10 job in the matrix runs, it should use this toxenv
+          - python: '3.10'
+            toxenv: py310-test
 
           - python: 3.9
             toxenv: py39-test-cov
diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index d6c650f76..ceb533f9f 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -27,6 +27,11 @@ jobs:
             python: 3.9
             toxenv: py39-test-cov
 
+          - name: Python 3.10
+            os: ubuntu-latest
+            python: '3.10'
+            toxenv: py310-test
+
           # Has to happen on ubuntu because galpy is finnicky on macOS
           - name: Python 3.9 with all optional dependencies
             os: ubuntu-latest
@@ -39,10 +44,10 @@ jobs:
             python: 3.9
             toxenv: nogsl
 
-          - name: Python 3.7 with oldest supported version of all dependencies
+          - name: Python 3.8 with oldest supported version of all dependencies
             os: ubuntu-latest
-            python: 3.7
-            toxenv: py37-test-oldestdeps
+            python: 3.8
+            toxenv: py38-test-oldestdeps
 
           # Mac and Windows:
           - name: Python 3.9 standard tests (macOS)
diff --git a/.github/workflows/wheels.yml b/.github/workflows/wheels.yml
index 413e808f1..e3a59c8d0 100644
--- a/.github/workflows/wheels.yml
+++ b/.github/workflows/wheels.yml
@@ -10,7 +10,7 @@ on:
 
 env:
   CIBW_BUILD: "cp3?-*"
-  CIBW_SKIP: "*-win32 *-manylinux_i686 cp35-* cp36-*"
+  CIBW_SKIP: "*-win32 *-manylinux_i686 cp35-* cp36-* cp37-*"
   CIBW_MANYLINUX_X86_64_IMAGE: manylinux2014
 
 jobs:
@@ -47,7 +47,7 @@ jobs:
 
       - name: Build wheels
         run: |
-          python -m pip install cibuildwheel==1.6.3
+          python -m pip install cibuildwheel
           python -m cibuildwheel --output-dir wheelhouse
 
       - uses: actions/upload-artifact@v2
diff --git a/gala/dynamics/lyapunov/dop853_lyapunov.pyx b/gala/dynamics/lyapunov/dop853_lyapunov.pyx
index 847574554..b9893650e 100644
--- a/gala/dynamics/lyapunov/dop853_lyapunov.pyx
+++ b/gala/dynamics/lyapunov/dop853_lyapunov.pyx
@@ -20,7 +20,7 @@ from ...potential.potential.cpotential cimport CPotentialWrapper
 from ...potential.frame.cframe cimport CFrameWrapper
 
 cdef extern from "frame/src/cframe.h":
-    ctypedef struct CFrame:
+    ctypedef struct CFrameType:
         pass
 
 cdef extern from "potential/src/cpotential.h":
@@ -29,10 +29,10 @@ cdef extern from "potential/src/cpotential.h":
 
 cdef extern from "dopri/dop853.h":
     ctypedef void (*FcnEqDiff)(unsigned n, double x, double *y, double *f,
-                              CPotential *p, CFrame *fr, unsigned norbits,
+                              CPotential *p, CFrameType *fr, unsigned norbits,
                               unsigned nbody, void *args) nogil
     void Fwrapper (unsigned ndim, double t, double *w, double *f,
-                   CPotential *p, CFrame *fr, unsigned norbits, unsigned nbody)
+                   CPotential *p, CFrameType *fr, unsigned norbits, unsigned nbody)
     double six_norm (double *x)
 
 cpdef dop853_lyapunov_max(hamiltonian, double[::1] w0,
@@ -62,7 +62,7 @@ cpdef dop853_lyapunov_max(hamiltonian, double[::1] w0,
 
         # whoa, so many dots
         CPotential cp = (<CPotentialWrapper>(hamiltonian.potential.c_instance)).cpotential
-        CFrame cf = (<CFrameWrapper>(hamiltonian.frame.c_instance)).cframe
+        CFrameType cf = (<CFrameWrapper>(hamiltonian.frame.c_instance)).cframe
 
         void *args
 
@@ -139,7 +139,7 @@ cpdef dop853_lyapunov_max_dont_save(hamiltonian, double[::1] w0,
 
         # whoa, so many dots
         CPotential cp = (<CPotentialWrapper>(hamiltonian.potential.c_instance)).cpotential
-        CFrame cf = (<CFrameWrapper>(hamiltonian.frame.c_instance)).cframe
+        CFrameType cf = (<CFrameWrapper>(hamiltonian.frame.c_instance)).cframe
 
         void *args
 
diff --git a/gala/dynamics/mockstream/mockstream.pyx b/gala/dynamics/mockstream/mockstream.pyx
index 4a29baf86..8beb5e0dd 100644
--- a/gala/dynamics/mockstream/mockstream.pyx
+++ b/gala/dynamics/mockstream/mockstream.pyx
@@ -27,7 +27,7 @@ from cpython.exc cimport PyErr_CheckSignals
 from ...integrate.cyintegrators.dop853 cimport (dop853_step,
                                                 dop853_helper_save_all)
 from ...potential.potential.cpotential cimport CPotentialWrapper, CPotential
-from ...potential.frame.cframe cimport CFrameWrapper, CFrame
+from ...potential.frame.cframe cimport CFrameWrapper, CFrameType
 from ...potential.potential.builtin.cybuiltin import NullWrapper
 
 from ...potential import Hamiltonian
@@ -43,11 +43,11 @@ __all__ = ['mockstream_dop853', 'mockstream_dop853_animate']
 
 cdef extern from "dopri/dop853.h":
     ctypedef void (*FcnEqDiff)(unsigned n, double x, double *y, double *f,
-                              CPotential *p, CFrame *fr,
+                              CPotential *p, CFrameType *fr,
                               unsigned norbits, unsigned nbody,
                               void *args) nogil
     void Fwrapper_direct_nbody(unsigned ndim, double t, double *w, double *f,
-                               CPotential *p, CFrame *fr,
+                               CPotential *p, CFrameType *fr,
                                unsigned norbits, unsigned nbody, void *args) nogil
 
 
@@ -94,7 +94,7 @@ cpdef mockstream_dop853(nbody, double[::1] time,
 
         # whoa, so many dots
         CPotential cp = (<CPotentialWrapper>(nbody.H.potential.c_instance)).cpotential
-        CFrame cf = (<CFrameWrapper>(nbody.H.frame.c_instance)).cframe
+        CFrameType cf = (<CFrameWrapper>(nbody.H.frame.c_instance)).cframe
 
         # for the test particles
         CPotentialWrapper null_wrapper = NullWrapper(1., [],
@@ -215,7 +215,7 @@ cpdef mockstream_dop853_animate(nbody, double[::1] t,
 
         # whoa, so many dots
         CPotential cp = (<CPotentialWrapper>(nbody.H.potential.c_instance)).cpotential
-        CFrame cf = (<CFrameWrapper>(nbody.H.frame.c_instance)).cframe
+        CFrameType cf = (<CFrameWrapper>(nbody.H.frame.c_instance)).cframe
 
         int nbodies = nbody._c_w0.shape[0] # includes the progenitor
         double [:, ::1] nbody_w0 = nbody._c_w0
diff --git a/gala/dynamics/nbody/nbody.pyx b/gala/dynamics/nbody/nbody.pyx
index b24fb4820..2e9b803f8 100644
--- a/gala/dynamics/nbody/nbody.pyx
+++ b/gala/dynamics/nbody/nbody.pyx
@@ -27,7 +27,7 @@ from ...integrate.cyintegrators.dop853 cimport (dop853_helper,
                                                 dop853_helper_save_all)
 
 cdef extern from "frame/src/cframe.h":
-    ctypedef struct CFrame:
+    ctypedef struct CFrameType:
         pass
 
 cdef extern from "potential/src/cpotential.h":
@@ -36,10 +36,10 @@ cdef extern from "potential/src/cpotential.h":
 
 cdef extern from "dopri/dop853.h":
     ctypedef void (*FcnEqDiff)(unsigned n, double x, double *y, double *f,
-                              CPotential *p, CFrame *fr, unsigned norbits,
+                              CPotential *p, CFrameType *fr, unsigned norbits,
                               unsigned nbody, void *args) nogil
     void Fwrapper_direct_nbody(unsigned ndim, double t, double *w, double *f,
-                               CPotential *p, CFrame *fr, unsigned norbits,
+                               CPotential *p, CFrameType *fr, unsigned norbits,
                                unsigned nbody, void *args)
 
 cpdef direct_nbody_dop853(double [:, ::1] w0, double[::1] t,
@@ -67,7 +67,7 @@ cpdef direct_nbody_dop853(double [:, ::1] w0, double[::1] t,
         void *args
         CPotential *c_particle_potentials[MAX_NBODY]
         CPotential cp = (<CPotentialWrapper>(hamiltonian.potential.c_instance)).cpotential
-        CFrame cf = (<CFrameWrapper>(hamiltonian.frame.c_instance)).cframe
+        CFrameType cf = (<CFrameWrapper>(hamiltonian.frame.c_instance)).cframe
 
     # Some input validation:
     if not isinstance(hamiltonian, Hamiltonian):
diff --git a/gala/integrate/cyintegrators/dop853.pxd b/gala/integrate/cyintegrators/dop853.pxd
index a73e2a7e0..03afb4873 100644
--- a/gala/integrate/cyintegrators/dop853.pxd
+++ b/gala/integrate/cyintegrators/dop853.pxd
@@ -1,7 +1,7 @@
 # cython: language_level=3
 
 cdef extern from "frame/src/cframe.h":
-    ctypedef struct CFrame:
+    ctypedef struct CFrameType:
         pass
 
 cdef extern from "potential/src/cpotential.h":
@@ -10,20 +10,20 @@ cdef extern from "potential/src/cpotential.h":
 
 cdef extern from "dopri/dop853.h":
     ctypedef void (*FcnEqDiff)(unsigned n, double x, double *y, double *f,
-                              CPotential *p, CFrame *fr, unsigned norbits,
+                              CPotential *p, CFrameType *fr, unsigned norbits,
                               unsigned nbody, void *args) nogil
 
-cdef void dop853_step(CPotential *cp, CFrame *cf, FcnEqDiff F,
+cdef void dop853_step(CPotential *cp, CFrameType *cf, FcnEqDiff F,
                       double *w, double t1, double t2, double dt0,
                       int ndim, int norbits, int nbody, void *args,
                       double atol, double rtol, int nmax)  except *
 
-cdef dop853_helper(CPotential *cp, CFrame *cf, FcnEqDiff F,
+cdef dop853_helper(CPotential *cp, CFrameType *cf, FcnEqDiff F,
                    double[:,::1] w0, double[::1] t,
                    int ndim, int norbits, int nbody, void *args, int ntimes,
                    double atol, double rtol, int nmax, int progress)
 
-cdef dop853_helper_save_all(CPotential *cp, CFrame *cf, FcnEqDiff F,
+cdef dop853_helper_save_all(CPotential *cp, CFrameType *cf, FcnEqDiff F,
                             double[:,::1] w0, double[::1] t,
                             int ndim, int norbits, int nbody, void *args,
                             int ntimes, double atol, double rtol, int nmax,
diff --git a/gala/integrate/cyintegrators/dop853.pyx b/gala/integrate/cyintegrators/dop853.pyx
index 3dcfc8327..385259dd4 100644
--- a/gala/integrate/cyintegrators/dop853.pyx
+++ b/gala/integrate/cyintegrators/dop853.pyx
@@ -22,7 +22,7 @@ from ...potential.potential.cpotential cimport CPotentialWrapper
 from ...potential.frame.cframe cimport CFrameWrapper
 
 cdef extern from "frame/src/cframe.h":
-    ctypedef struct CFrame:
+    ctypedef struct CFrameType:
         pass
 
 cdef extern from "potential/src/cpotential.h":
@@ -33,14 +33,14 @@ cdef extern from "potential/src/cpotential.h":
 
 cdef extern from "dopri/dop853.h":
     ctypedef void (*FcnEqDiff)(unsigned n, double x, double *y, double *f,
-                              CPotential *p, CFrame *fr, unsigned norbits,
+                              CPotential *p, CFrameType *fr, unsigned norbits,
                               unsigned nbody, void *args) nogil
     ctypedef void (*SolTrait)(long nr, double xold, double x, double* y,
                               unsigned n, int* irtrn)
 
     # See dop853.h for full description of all input parameters
     int dop853 (unsigned n, FcnEqDiff fn,
-                CPotential *p, CFrame *fr, unsigned n_orbits, unsigned nbody,
+                CPotential *p, CFrameType *fr, unsigned n_orbits, unsigned nbody,
                 void *args,
                 double x, double* y, double xend,
                 double* rtoler, double* atoler, int itoler, SolTrait solout,
@@ -49,7 +49,7 @@ cdef extern from "dopri/dop853.h":
                 long nstiff, unsigned nrdens, unsigned* icont, unsigned licont)
 
     void Fwrapper (unsigned ndim, double t, double *w, double *f,
-                   CPotential *p, CFrame *fr, unsigned norbits)
+                   CPotential *p, CFrameType *fr, unsigned norbits)
 
 cdef extern from "stdio.h":
     ctypedef struct FILE
@@ -59,7 +59,7 @@ cdef void solout(long nr, double xold, double x, double* y, unsigned n, int* irt
     # TODO: see here for example in FORTRAN: http://www.unige.ch/~hairer/prog/nonstiff/dr_dop853.f
     pass
 
-cdef void dop853_step(CPotential *cp, CFrame *cf, FcnEqDiff F,
+cdef void dop853_step(CPotential *cp, CFrameType *cf, FcnEqDiff F,
                       double *w, double t1, double t2, double dt0,
                       int ndim, int norbits, int nbody, void *args,
                       double atol, double rtol, int nmax) except *:
@@ -80,7 +80,7 @@ cdef void dop853_step(CPotential *cp, CFrame *cf, FcnEqDiff F,
     elif res == -4:
         raise RuntimeError("The problem is probably stiff (interrupted).")
 
-cdef dop853_helper(CPotential *cp, CFrame *cf, FcnEqDiff F,
+cdef dop853_helper(CPotential *cp, CFrameType *cf, FcnEqDiff F,
                    double[:, ::1] w0, double[::1] t,
                    int ndim, int norbits, int nbody, void *args, int ntimes,
                    double atol, double rtol, int nmax, int progress):
@@ -128,7 +128,7 @@ cdef dop853_helper(CPotential *cp, CFrame *cf, FcnEqDiff F,
 
     return w
 
-cdef dop853_helper_save_all(CPotential *cp, CFrame *cf, FcnEqDiff F,
+cdef dop853_helper_save_all(CPotential *cp, CFrameType *cf, FcnEqDiff F,
                             double[:, ::1] w0, double[::1] t,
                             int ndim, int norbits, int nbody, void *args,
                             int ntimes, double atol, double rtol, int nmax,
@@ -207,7 +207,7 @@ cpdef dop853_integrate_hamiltonian(hamiltonian, double[:, ::1] w0, double[::1] t
 
         # whoa, so many dots
         CPotential cp = (<CPotentialWrapper>(hamiltonian.potential.c_instance)).cpotential
-        CFrame cf = (<CFrameWrapper>(hamiltonian.frame.c_instance)).cframe
+        CFrameType cf = (<CFrameWrapper>(hamiltonian.frame.c_instance)).cframe
 
     # 0 below is for nbody - we ignore that in this test particle integration
     all_w = dop853_helper_save_all(&cp, &cf, <FcnEqDiff> Fwrapper,
diff --git a/gala/integrate/cyintegrators/dopri/dop853.c b/gala/integrate/cyintegrators/dopri/dop853.c
index c01d98423..7de6a1128 100644
--- a/gala/integrate/cyintegrators/dopri/dop853.c
+++ b/gala/integrate/cyintegrators/dopri/dop853.c
@@ -78,7 +78,7 @@ static double max_d (double a, double b)
 } /* max_d */
 
 
-static double hinit (unsigned n, FcnEqDiff fcn, CPotential *p, CFrame *fr, unsigned norbits, unsigned nbody, void *args,
+static double hinit (unsigned n, FcnEqDiff fcn, CPotential *p, CFrameType *fr, unsigned norbits, unsigned nbody, void *args,
         double x, double* y,
 	      double posneg, double* f0, double* f1, double* yy1, int iord,
 	      double hmax, double* atoler, double* rtoler, int itoler)
@@ -155,7 +155,7 @@ static double hinit (unsigned n, FcnEqDiff fcn, CPotential *p, CFrame *fr, unsig
 
 
 /* core integrator */
-static int dopcor (unsigned n, FcnEqDiff fcn, CPotential *p, CFrame *fr, unsigned norbits, unsigned nbody, void *args,
+static int dopcor (unsigned n, FcnEqDiff fcn, CPotential *p, CFrameType *fr, unsigned norbits, unsigned nbody, void *args,
        double x, double* y, double xend,
 		   double hmax, double h, double* rtoler, double* atoler,
 		   int itoler, FILE* fileout, SolTrait solout, int iout,
@@ -695,7 +695,7 @@ static int dopcor (unsigned n, FcnEqDiff fcn, CPotential *p, CFrame *fr, unsigne
 
 /* front-end */
 int dop853
- (unsigned n, FcnEqDiff fcn, CPotential *p, CFrame *fr, unsigned norbits, unsigned nbody, void *args,
+ (unsigned n, FcnEqDiff fcn, CPotential *p, CFrameType *fr, unsigned norbits, unsigned nbody, void *args,
   double x, double* y, double xend, double* rtoler,
   double* atoler, int itoler, SolTrait solout, int iout, FILE* fileout, double uround,
   double safe, double fac1, double fac2, double beta, double hmax, double h,
@@ -977,7 +977,7 @@ double contd8 (unsigned ii, double x)
 
 /* ADDED BY APW */
 void Fwrapper (unsigned full_ndim, double t, double *w, double *f,
-               CPotential *p, CFrame *fr, unsigned norbits, unsigned na,
+               CPotential *p, CFrameType *fr, unsigned norbits, unsigned na,
                void *args) {
     /* na can be ignored here - used in nbody wrapper below */
 
@@ -991,7 +991,7 @@ void Fwrapper (unsigned full_ndim, double t, double *w, double *f,
 }
 
 void Fwrapper_direct_nbody (unsigned full_ndim, double t, double *w, double *f,
-                            CPotential *p, CFrame *fr,
+                            CPotential *p, CFrameType *fr,
                             unsigned norbits, unsigned nbody,
                             void *args) {
     /* Here, the extra args are actually the array of CPotential objects that
diff --git a/gala/integrate/cyintegrators/dopri/dop853.h b/gala/integrate/cyintegrators/dopri/dop853.h
index 564038c5f..d220ac2c8 100644
--- a/gala/integrate/cyintegrators/dopri/dop853.h
+++ b/gala/integrate/cyintegrators/dopri/dop853.h
@@ -188,7 +188,7 @@ nfcnRead    Number of function calls.
 #include "hamiltonian/src/chamiltonian.h"
 
 typedef void (*FcnEqDiff)(unsigned n, double x, double *y, double *f,
-                          CPotential *p, CFrame *fr, unsigned norbits,
+                          CPotential *p, CFrameType *fr, unsigned norbits,
                           unsigned nbody, void *args);
 
 typedef void (*SolTrait)(long nr, double xold, double x, double* y, unsigned n, int* irtrn);
@@ -197,7 +197,7 @@ extern int dop853
  (unsigned n,      /* dimension of the system <= UINT_MAX-1*/
   FcnEqDiff fcn,   /* function computing the value of f(x,y) */
   CPotential *p,   /* ADDED BY ADRN: parameters for gradient function */
-  CFrame *fr,       /* ADDED BY ADRN: reference frame */
+  CFrameType *fr,       /* ADDED BY ADRN: reference frame */
   unsigned n_orbits, /* ADDED BY ADRN: total number of orbits, i.e. bodies */
   unsigned n_body, /* ADDED BY ADRN: number of nbody particles */
   void *args,      /* ADDED BY ADRN: a container for other stuff */
@@ -239,10 +239,10 @@ extern double xRead (void);
 
 /* ADDED BY APW */
 extern void Fwrapper (unsigned ndim, double t, double *w, double *f,
-                      CPotential *p, CFrame *fr,
+                      CPotential *p, CFrameType *fr,
                       unsigned norbits, unsigned nbody, void *args);
 extern void Fwrapper_direct_nbody(unsigned ndim, double t, double *w, double *f,
-                                  CPotential *p, CFrame *fr,
+                                  CPotential *p, CFrameType *fr,
                                   unsigned norbits, unsigned nbody,
                                   void *args); // here args becomes the particle potentials
 extern double six_norm (double *x); /* Needed for Lyapunov */
diff --git a/gala/integrate/cyintegrators/leapfrog.pyx b/gala/integrate/cyintegrators/leapfrog.pyx
index 5274b4b0e..5e37b054b 100644
--- a/gala/integrate/cyintegrators/leapfrog.pyx
+++ b/gala/integrate/cyintegrators/leapfrog.pyx
@@ -17,7 +17,7 @@ from ...potential.potential.cpotential cimport CPotentialWrapper
 from ...potential.frame import StaticFrame
 
 cdef extern from "frame/src/cframe.h":
-    ctypedef struct CFrame:
+    ctypedef struct CFrameType:
         pass
 
 cdef extern from "potential/src/cpotential.h":
diff --git a/gala/integrate/cyintegrators/ruth4.pyx b/gala/integrate/cyintegrators/ruth4.pyx
index 32ce86981..c6f62e6ed 100644
--- a/gala/integrate/cyintegrators/ruth4.pyx
+++ b/gala/integrate/cyintegrators/ruth4.pyx
@@ -17,7 +17,7 @@ from ...potential.potential.cpotential cimport CPotentialWrapper
 from ...potential.frame import StaticFrame
 
 cdef extern from "frame/src/cframe.h":
-    ctypedef struct CFrame:
+    ctypedef struct CFrameType:
         pass
 
 cdef extern from "potential/src/cpotential.h":
diff --git a/gala/potential/frame/builtin/frames.pyx b/gala/potential/frame/builtin/frames.pyx
index e2c83aa92..d05b7171f 100644
--- a/gala/potential/frame/builtin/frames.pyx
+++ b/gala/potential/frame/builtin/frames.pyx
@@ -24,7 +24,7 @@ cdef extern from "src/funcdefs.h":
     ctypedef void (*hessianfunc)(double t, double *pars, double *q, int n_dim, double *hess) nogil
 
 cdef extern from "frame/src/cframe.h":
-    ctypedef struct CFrame:
+    ctypedef struct CFrameType:
         energyfunc energy
         gradientfunc gradient
         hessianfunc hessian
@@ -50,7 +50,7 @@ __all__ = ['StaticFrame', 'ConstantRotatingFrame']
 cdef class StaticFrameWrapper(CFrameWrapper):
 
     def __init__(self, list params):
-        cdef CFrame cf
+        cdef CFrameType cf
 
         self.init(params)
 
@@ -87,7 +87,7 @@ cdef class ConstantRotatingFrameWrapper2D(CFrameWrapper):
 
     def __init__(self, list params):
         cdef:
-            CFrame cf
+            CFrameType cf
 
         assert len(params) == 1
         self._params = np.array([params[0]], dtype=np.float64)
@@ -104,7 +104,7 @@ cdef class ConstantRotatingFrameWrapper3D(CFrameWrapper):
 
     def __init__(self, list params):
         cdef:
-            CFrame cf
+            CFrameType cf
 
         assert len(params) == 3
         self._params = np.array([params[0], params[1], params[2]],
diff --git a/gala/potential/frame/cframe.pxd b/gala/potential/frame/cframe.pxd
index f39ab9298..8570d4757 100644
--- a/gala/potential/frame/cframe.pxd
+++ b/gala/potential/frame/cframe.pxd
@@ -1,15 +1,15 @@
 # cython: language_level=3
 
 cdef extern from "frame/src/cframe.h":
-    ctypedef struct CFrame:
+    ctypedef struct CFrameType:
         pass
 
-    double frame_hamiltonian(CFrame *fr, double t, double *qp, int n_dim) nogil
-    void frame_gradient(CFrame *fr, double t, double *qp, int n_dim, double *dH) nogil
-    void frame_hessian(CFrame *fr, double t, double *qp, int n_dim, double *d2H) nogil
+    double frame_hamiltonian(CFrameType *fr, double t, double *qp, int n_dim) nogil
+    void frame_gradient(CFrameType *fr, double t, double *qp, int n_dim, double *dH) nogil
+    void frame_hessian(CFrameType *fr, double t, double *qp, int n_dim, double *d2H) nogil
 
 cdef class CFrameWrapper:
-    cdef CFrame cframe
+    cdef CFrameType cframe
     cdef double[::1] _params
     cpdef init(self, list parameters)
     cpdef energy(self, double[:,::1] w, double[::1] t)
diff --git a/gala/potential/frame/cframe.pyx b/gala/potential/frame/cframe.pyx
index 26b9b8be6..7d95c3e03 100644
--- a/gala/potential/frame/cframe.pyx
+++ b/gala/potential/frame/cframe.pyx
@@ -31,7 +31,7 @@ cdef class CFrameWrapper:
         """
         cdef:
             int n, ndim, i
-            CFrame cf = self.cframe
+            CFrameType cf = self.cframe
         n, ndim = _validate_pos_arr(w)
 
         cdef double [::1] pot = np.zeros(n)
@@ -51,7 +51,7 @@ cdef class CFrameWrapper:
         """
         cdef:
             int n, ndim, i
-            CFrame cf = self.cframe
+            CFrameType cf = self.cframe
         n, ndim = _validate_pos_arr(w)
 
         cdef double[:, ::1] dH = np.zeros((n, ndim))
@@ -71,7 +71,7 @@ cdef class CFrameWrapper:
         """
         cdef:
             int n, ndim, i
-            CFrame cf = self.cframe
+            CFrameType cf = self.cframe
         n, ndim = _validate_pos_arr(w)
 
         cdef double[:, :, ::1] d2H = np.zeros((n, ndim, ndim))
diff --git a/gala/potential/frame/src/cframe.c b/gala/potential/frame/src/cframe.c
index c4beccb13..f8d10f0a0 100644
--- a/gala/potential/frame/src/cframe.c
+++ b/gala/potential/frame/src/cframe.c
@@ -1,15 +1,15 @@
 #include "frame/src/cframe.h"
 
-double frame_hamiltonian(CFrame *fr, double t, double *qp, int n_dim) {
+double frame_hamiltonian(CFrameType *fr, double t, double *qp, int n_dim) {
     double v = (fr->energy)(t, (fr->parameters), qp, n_dim);
     return v;
 }
 
-void frame_gradient(CFrame *fr, double t, double *qp, int n_dim, double *dH) {
+void frame_gradient(CFrameType *fr, double t, double *qp, int n_dim, double *dH) {
     (fr->gradient)(t, (fr->parameters), qp, n_dim, dH);
 }
 
-void frame_hessian(CFrame *fr, double t, double *qp, int n_dim, double *d2H) {
+void frame_hessian(CFrameType *fr, double t, double *qp, int n_dim, double *d2H) {
     // TODO: not implemented!!
     // TODO: can I just add in the terms from the frame here?
     // (fr->hessian)(t, (fr->parameters), qp, n_dim, d2H);
diff --git a/gala/potential/frame/src/cframe.h b/gala/potential/frame/src/cframe.h
index a15008cb6..92ddf2521 100644
--- a/gala/potential/frame/src/cframe.h
+++ b/gala/potential/frame/src/cframe.h
@@ -2,9 +2,9 @@
 
 #ifndef _CFRAME_H
 #define _CFRAME_H
-    typedef struct _CFrame CFrame;
+    // typedef struct CFrameType CFrame;
 
-    struct _CFrame {
+    typedef struct {
         // arrays of pointers to each of the function types above
         energyfunc energy;
         gradientfunc gradient;
@@ -14,9 +14,9 @@
 
         // pointer to the parameter array
         double *parameters;
-    };
+    } CFrameType;
 #endif
 
-extern double frame_hamiltonian(CFrame *fr, double t, double *qp, int n_dim);
-extern void frame_gradient(CFrame *fr, double t, double *qp, int n_dim, double *dH);
-extern void frame_hessian(CFrame *fr, double t, double *qp, int n_dim, double *d2H);
+extern double frame_hamiltonian(CFrameType *fr, double t, double *qp, int n_dim);
+extern void frame_gradient(CFrameType *fr, double t, double *qp, int n_dim, double *dH);
+extern void frame_hessian(CFrameType *fr, double t, double *qp, int n_dim, double *d2H);
diff --git a/gala/potential/hamiltonian/src/chamiltonian.c b/gala/potential/hamiltonian/src/chamiltonian.c
index e7d0775e7..02f49f1b6 100644
--- a/gala/potential/hamiltonian/src/chamiltonian.c
+++ b/gala/potential/hamiltonian/src/chamiltonian.c
@@ -2,7 +2,7 @@
 #include "potential/src/cpotential.h"
 #include "frame/src/cframe.h"
 
-double hamiltonian_value(CPotential *p, CFrame *fr, double t, double *qp) {
+double hamiltonian_value(CPotential *p, CFrameType *fr, double t, double *qp) {
     double v = 0;
     int i;
 
@@ -16,7 +16,7 @@ double hamiltonian_value(CPotential *p, CFrame *fr, double t, double *qp) {
     return v;
 }
 
-void hamiltonian_gradient(CPotential *p, CFrame *fr, double t, double *qp, double *dH) {
+void hamiltonian_gradient(CPotential *p, CFrameType *fr, double t, double *qp, double *dH) {
     int i;
 
     for (i=0; i < 2*(p->n_dim); i++) {
@@ -33,7 +33,7 @@ void hamiltonian_gradient(CPotential *p, CFrame *fr, double t, double *qp, doubl
     }
 }
 
-void hamiltonian_hessian(CPotential *p, CFrame *fr, double t, double *qp, double *d2H) {
+void hamiltonian_hessian(CPotential *p, CFrameType *fr, double t, double *qp, double *d2H) {
     int i;
 
     for (i=0; i < p->n_components; i++) {
diff --git a/gala/potential/hamiltonian/src/chamiltonian.h b/gala/potential/hamiltonian/src/chamiltonian.h
index d9f08b9b7..fdcf47131 100644
--- a/gala/potential/hamiltonian/src/chamiltonian.h
+++ b/gala/potential/hamiltonian/src/chamiltonian.h
@@ -1,6 +1,6 @@
 #include "potential/src/cpotential.h"
 #include "frame/src/cframe.h"
 
-extern double hamiltonian_value(CPotential *p, CFrame *fr, double t, double *q);
-extern void hamiltonian_gradient(CPotential *p, CFrame *fr, double t, double *q, double *grad);
-extern void hamiltonian_hessian(CPotential *p, CFrame *fr, double t, double *q, double *hess);
+extern double hamiltonian_value(CPotential *p, CFrameType *fr, double t, double *q);
+extern void hamiltonian_gradient(CPotential *p, CFrameType *fr, double t, double *q, double *grad);
+extern void hamiltonian_hessian(CPotential *p, CFrameType *fr, double t, double *q, double *hess);
diff --git a/gala/potential/scf/tests/test_accp_fortran.py b/gala/potential/scf/tests/test_accp_fortran.py
index c17eaff7f..ad2726a18 100644
--- a/gala/potential/scf/tests/test_accp_fortran.py
+++ b/gala/potential/scf/tests/test_accp_fortran.py
@@ -2,7 +2,7 @@
 
 # Standard library
 import os
-from math import factorial
+from math import factorial as _factorial
 
 # Third-party
 from astropy.constants import G as _G
@@ -22,13 +22,19 @@
                 allow_module_level=True)
 
 
+def factorial(x):
+    return _factorial(int(x))
+
+
 @pytest.mark.parametrize("basename", [
     'simple-hernquist', 'multi-hernquist', 'simple-nonsph', 'random', 'wang-zhao',
 ])
 def test_density(basename):
     pos_path = os.path.abspath(get_pkg_data_filename('data/positions.dat.gz'))
-    coeff_path = os.path.abspath(get_pkg_data_filename('data/{0}.coeff'.format(basename)))
-    accp_path = os.path.abspath(get_pkg_data_filename('data/{0}-accp.dat.gz'.format(basename)))
+    coeff_path = os.path.abspath(
+        get_pkg_data_filename(f'data/{basename}.coeff'))
+    accp_path = os.path.abspath(
+        get_pkg_data_filename(f'data/{basename}-accp.dat.gz'))
 
     xyz = np.ascontiguousarray(np.loadtxt(pos_path, skiprows=1).T)
     coeff = np.atleast_2d(np.loadtxt(coeff_path, skiprows=1))
diff --git a/gala/potential/scf/tests/test_computecoeff_fortran.py b/gala/potential/scf/tests/test_computecoeff_fortran.py
index 2bfcfe182..26435731c 100644
--- a/gala/potential/scf/tests/test_computecoeff_fortran.py
+++ b/gala/potential/scf/tests/test_computecoeff_fortran.py
@@ -2,7 +2,7 @@
 
 # Standard library
 import os
-from math import factorial
+from math import factorial as _factorial
 
 # Third-party
 from astropy.utils.data import get_pkg_data_filename
@@ -20,6 +20,10 @@
 # Compare coefficients computed with Fortran to Biff
 
 
+def factorial(x):
+    return _factorial(int(x))
+
+
 @pytest.mark.parametrize("basename", [
     'hernquist'
 ])
diff --git a/setup.cfg b/setup.cfg
index f5e271bba..a1776c763 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -9,19 +9,19 @@ license_file = LICENSE
 url = http://gala.adrian.pw/
 edit_on_github = False
 github_project = adrn/gala
-python_requires = ">=3.7"
+python_requires = ">=3.8"
 
 [options]
 zip_safe = False
 packages = find:
 install_requires =
-    numpy>=1.17
+    numpy>=1.20
     astropy>=4.2
     pyyaml
     cython>=0.29
-    scipy>=1.2
+    scipy>=1.6
     packaging
-python_requires = >=3.7
+python_requires = >=3.8
 setup_requires =
     setuptools_scm
     extension-helpers
diff --git a/tox.ini b/tox.ini
index d8cf21a7c..55ad58cd5 100644
--- a/tox.ini
+++ b/tox.ini
@@ -2,7 +2,7 @@
 
 [tox]
 envlist =
-    py{37,38,39}-test{,-extradeps,-devdeps,-oldestdeps}{,-cov}
+    py{38,39,310}-test{,-extradeps,-devdeps,-oldestdeps}{,-cov}
     codestyle
     nogsl
 
@@ -42,10 +42,10 @@ description =
 deps =
     # The oldestdeps factor is intended to be used to install the oldest
     # versions of all dependencies that have a minimum version.
-    oldestdeps: numpy==1.18.*
-    oldestdeps: matplotlib==3.0.*
-    oldestdeps: scipy==1.4.*
-    oldestdeps: astropy==4.0.*
+    oldestdeps: numpy==1.20.*
+    oldestdeps: matplotlib==3.4.*
+    oldestdeps: scipy==1.6.*
+    oldestdeps: astropy==4.2.*
 
     devdeps: :NIGHTLY:numpy
     devdeps: git+https://github.com/astropy/astropy.git#egg=astropy