diff --git a/std/compress/lzss_v2/average_block.hex b/std/compress/lzss/average_block.hex
similarity index 100%
rename from std/compress/lzss_v2/average_block.hex
rename to std/compress/lzss/average_block.hex
diff --git a/std/compress/lzss_v2/backref.go b/std/compress/lzss/backref.go
similarity index 99%
rename from std/compress/lzss_v2/backref.go
rename to std/compress/lzss/backref.go
index ffb67611c8..6047c3d692 100644
--- a/std/compress/lzss_v2/backref.go
+++ b/std/compress/lzss/backref.go
@@ -1,4 +1,4 @@
-package lzss_v2
+package lzss
 
 import (
 	"math"
diff --git a/std/compress/lzss_v2/compile_large/main.go b/std/compress/lzss/compile_large/main.go
similarity index 70%
rename from std/compress/lzss_v2/compile_large/main.go
rename to std/compress/lzss/compile_large/main.go
index aab790565f..8932d518ae 100644
--- a/std/compress/lzss_v2/compile_large/main.go
+++ b/std/compress/lzss/compile_large/main.go
@@ -3,7 +3,7 @@ package main
 import (
 	"fmt"
 	"github.com/consensys/gnark/std/compress"
-	"github.com/consensys/gnark/std/compress/lzss_v2"
+	"github.com/consensys/gnark/std/compress/lzss"
 )
 
 // executable to generate the constraints for the circuit and store it
@@ -14,7 +14,7 @@ func check(e error) {
 }
 
 func main() {
-	cs, err := lzss_v2.BenchCompressionE2ECompilation(nil, "../../test_cases/large")
+	cs, err := lzss.BenchCompressionE2ECompilation(nil, "../../test_cases/large")
 	check(err)
 
 	fmt.Println(cs.GetNbConstraints(), "constraints")
diff --git a/std/compress/lzss_v2/compress.go b/std/compress/lzss/compress.go
similarity index 90%
rename from std/compress/lzss_v2/compress.go
rename to std/compress/lzss/compress.go
index 656cf0fcae..6f8d921b61 100644
--- a/std/compress/lzss_v2/compress.go
+++ b/std/compress/lzss/compress.go
@@ -1,11 +1,11 @@
-package lzss_v2
+package lzss
 
 import (
 	"bytes"
 	"fmt"
 	"math/bits"
 
-	"github.com/consensys/gnark/std/compress/lzss_v2/suffixarray"
+	"github.com/consensys/gnark/std/compress/lzss/suffixarray"
 	"github.com/icza/bitio"
 )
 
@@ -22,8 +22,17 @@ type Compressor struct {
 	dictSa    [maxDictSize]int32 // suffix array space.
 }
 
+type CompressionMode uint8
+
+const (
+	BestCompression        CompressionMode = 1
+	GoodCompression        CompressionMode = 2
+	GoodSnarkDecompression CompressionMode = 4
+	BestSnarkDecompression CompressionMode = 8
+)
+
 // NewCompressor returns a new compressor with the given dictionary
-func NewCompressor(dict []byte) (*Compressor, error) {
+func NewCompressor(dict []byte, compressionMode CompressionMode) (*Compressor, error) {
 	dict = augmentDict(dict)
 	if len(dict) > maxDictSize {
 		return nil, fmt.Errorf("dict size must be <= %d", maxDictSize)
@@ -40,8 +49,8 @@ func augmentDict(dict []byte) []byte {
 	return append(dict, symbolDict, symbolShort, symbolLong)
 }
 
-func initDictBackref(dict []byte) backrefType {
-	addrNbBits := uint8(bits.Len(uint(len(dict))))
+func (compressor *Compressor) initDictBackref() backrefType {
+	addrNbBits := uint8(bits.Len(uint(len(compressor.dictData))))
 	return newBackRefType(symbolDict, (addrNbBits+forceDivisibleBy-1)/forceDivisibleBy*forceDivisibleBy, 8, true)
 }
 
@@ -59,7 +68,7 @@ func (compressor *Compressor) Compress(d []byte) (c []byte, err error) {
 	// build the index
 	compressor.inputIndex = suffixarray.New(d, compressor.inputSa[:len(d)])
 
-	dictBackRefType := initDictBackref(compressor.dictData)
+	dictBackRefType := compressor.initDictBackref()
 
 	bDict := backref{bType: dictBackRefType, length: -1, offset: -1}
 	bShort := backref{bType: shortBackRefType, length: -1, offset: -1}
diff --git a/std/compress/lzss_v2/compress_test.go b/std/compress/lzss/compress_test.go
similarity index 99%
rename from std/compress/lzss_v2/compress_test.go
rename to std/compress/lzss/compress_test.go
index 5f95e88b09..ddfcf01fb3 100644
--- a/std/compress/lzss_v2/compress_test.go
+++ b/std/compress/lzss/compress_test.go
@@ -1,4 +1,4 @@
-package lzss_v2
+package lzss
 
 import (
 	"bytes"
diff --git a/std/compress/lzss_v2/decompress.go b/std/compress/lzss/decompress.go
similarity index 99%
rename from std/compress/lzss_v2/decompress.go
rename to std/compress/lzss/decompress.go
index 403b1d6220..82151f8ae1 100644
--- a/std/compress/lzss_v2/decompress.go
+++ b/std/compress/lzss/decompress.go
@@ -1,4 +1,4 @@
-package lzss_v2
+package lzss
 
 import (
 	"bytes"
diff --git a/std/compress/lzss_v2/dict_fun b/std/compress/lzss/dict_fun
similarity index 100%
rename from std/compress/lzss_v2/dict_fun
rename to std/compress/lzss/dict_fun
diff --git a/std/compress/lzss_v2/dict_naive b/std/compress/lzss/dict_naive
similarity index 100%
rename from std/compress/lzss_v2/dict_naive
rename to std/compress/lzss/dict_naive
diff --git a/std/compress/lzss_v2/e2e_test.go b/std/compress/lzss/e2e_test.go
similarity index 99%
rename from std/compress/lzss_v2/e2e_test.go
rename to std/compress/lzss/e2e_test.go
index 13d3b012f6..f0759ef37e 100644
--- a/std/compress/lzss_v2/e2e_test.go
+++ b/std/compress/lzss/e2e_test.go
@@ -1,4 +1,4 @@
-package lzss_v2
+package lzss
 
 import (
 	"github.com/consensys/gnark-crypto/ecc"
diff --git a/std/compress/lzss_v2/snark.go b/std/compress/lzss/snark.go
similarity index 99%
rename from std/compress/lzss_v2/snark.go
rename to std/compress/lzss/snark.go
index abc7a61ee3..be4c71b32b 100644
--- a/std/compress/lzss_v2/snark.go
+++ b/std/compress/lzss/snark.go
@@ -1,4 +1,4 @@
-package lzss_v2
+package lzss
 
 import (
 	"fmt"
diff --git a/std/compress/lzss_v2/snark_test.go b/std/compress/lzss/snark_test.go
similarity index 99%
rename from std/compress/lzss_v2/snark_test.go
rename to std/compress/lzss/snark_test.go
index 045a285ab8..d1bfba7360 100644
--- a/std/compress/lzss_v2/snark_test.go
+++ b/std/compress/lzss/snark_test.go
@@ -1,4 +1,4 @@
-package lzss_v2
+package lzss
 
 import (
 	"bytes"
diff --git a/std/compress/lzss_v2/snark_testing.go b/std/compress/lzss/snark_testing.go
similarity index 99%
rename from std/compress/lzss_v2/snark_testing.go
rename to std/compress/lzss/snark_testing.go
index 62ed79ab4d..292cd999d3 100644
--- a/std/compress/lzss_v2/snark_testing.go
+++ b/std/compress/lzss/snark_testing.go
@@ -1,4 +1,4 @@
-package lzss_v2
+package lzss
 
 import (
 	"fmt"
diff --git a/std/compress/lzss_v2/suffixarray/sais.go b/std/compress/lzss/suffixarray/sais.go
similarity index 100%
rename from std/compress/lzss_v2/suffixarray/sais.go
rename to std/compress/lzss/suffixarray/sais.go
diff --git a/std/compress/lzss_v2/suffixarray/sais2.go b/std/compress/lzss/suffixarray/sais2.go
similarity index 100%
rename from std/compress/lzss_v2/suffixarray/sais2.go
rename to std/compress/lzss/suffixarray/sais2.go
diff --git a/std/compress/lzss_v2/suffixarray/suffixarray.go b/std/compress/lzss/suffixarray/suffixarray.go
similarity index 100%
rename from std/compress/lzss_v2/suffixarray/suffixarray.go
rename to std/compress/lzss/suffixarray/suffixarray.go
diff --git a/std/compress/lzss_v2/testdata/fuzz/FuzzCompress/6ed62c91940dd97f b/std/compress/lzss/testdata/fuzz/FuzzCompress/6ed62c91940dd97f
similarity index 100%
rename from std/compress/lzss_v2/testdata/fuzz/FuzzCompress/6ed62c91940dd97f
rename to std/compress/lzss/testdata/fuzz/FuzzCompress/6ed62c91940dd97f
diff --git a/std/compress/lzss_v2/testdata/fuzz/FuzzCompress/e3443030b91d09bb b/std/compress/lzss/testdata/fuzz/FuzzCompress/e3443030b91d09bb
similarity index 100%
rename from std/compress/lzss_v2/testdata/fuzz/FuzzCompress/e3443030b91d09bb
rename to std/compress/lzss/testdata/fuzz/FuzzCompress/e3443030b91d09bb