diff --git a/go.mod b/go.mod
index ff34417136..2acc9523bb 100644
--- a/go.mod
+++ b/go.mod
@@ -6,7 +6,7 @@ require (
 	github.com/bits-and-blooms/bitset v1.8.0
 	github.com/blang/semver/v4 v4.0.0
 	github.com/consensys/bavard v0.1.13
-	github.com/consensys/compress v0.1.0
+	github.com/consensys/compress v0.2.1-0.20240103160955-e4fcce3dc96a
 	github.com/consensys/gnark-crypto v0.12.2-0.20231221171913-5d5eded6bb15
 	github.com/fxamacker/cbor/v2 v2.5.0
 	github.com/google/go-cmp v0.5.9
diff --git a/go.sum b/go.sum
index 138bb12567..d11680dab2 100644
--- a/go.sum
+++ b/go.sum
@@ -4,8 +4,10 @@ github.com/blang/semver/v4 v4.0.0 h1:1PFHFE6yCCTv8C1TeyNNarDzntLi7wMI5i/pzqYIsAM
 github.com/blang/semver/v4 v4.0.0/go.mod h1:IbckMUScFkM3pff0VJDNKRiT6TG/YpiHIM2yvyW5YoQ=
 github.com/consensys/bavard v0.1.13 h1:oLhMLOFGTLdlda/kma4VOJazblc7IM5y5QPd2A/YjhQ=
 github.com/consensys/bavard v0.1.13/go.mod h1:9ItSMtA/dXMAiL7BG6bqW2m3NdSEObYWoH223nGHukI=
-github.com/consensys/compress v0.1.0 h1:fczDaganmx2198GudPo4+5VX3eBvKy/bEJfmNotbr70=
-github.com/consensys/compress v0.1.0/go.mod h1:Ne8+cGKjqgjF1dlHapZx38pHzWpaBYhsKxQa+JPl0zM=
+github.com/consensys/compress v0.2.0 h1:aBg3YJe8ZFUxm/RF+ppx/URFsZq3aJ6o8isLDQysYDA=
+github.com/consensys/compress v0.2.0/go.mod h1:Ne8+cGKjqgjF1dlHapZx38pHzWpaBYhsKxQa+JPl0zM=
+github.com/consensys/compress v0.2.1-0.20240103160955-e4fcce3dc96a h1:0Y7y1JXtP8O/nL7LHpBt62pGZ87so63uWrYqUoq920s=
+github.com/consensys/compress v0.2.1-0.20240103160955-e4fcce3dc96a/go.mod h1:Ne8+cGKjqgjF1dlHapZx38pHzWpaBYhsKxQa+JPl0zM=
 github.com/consensys/gnark-crypto v0.12.2-0.20231221171913-5d5eded6bb15 h1:mcxhrDtXKIepsKXofxSuXRst+41yzAcoNWKIotsjMTQ=
 github.com/consensys/gnark-crypto v0.12.2-0.20231221171913-5d5eded6bb15/go.mod h1:wKqwsieaKPThcFkHe0d0zMsbHEUWFmZcG7KBCse210o=
 github.com/coreos/go-systemd/v22 v22.5.0/go.mod h1:Y58oyj3AT4RCenI/lSvhwexgC+NSVTIJ3seZv2GcEnc=
diff --git a/std/compress/lzss/snark.go b/std/compress/lzss/snark.go
index 198cb739df..3ac58fabe4 100644
--- a/std/compress/lzss/snark.go
+++ b/std/compress/lzss/snark.go
@@ -25,13 +25,15 @@ func Decompress(api frontend.API, c []frontend.Variable, cLength frontend.Variab
 	dictBrNbWords := int(dictBackRefType.NbBitsBackRef) / wordNbBits
 	byteNbWords := 8 / wordNbBits
 
-	api.AssertIsEqual(compress.ReadNum(api, c, byteNbWords, wordNbBits), 0) // compressor version TODO @tabaie @gbotrel Handle this outside the circuit instead?
-	fileCompressionMode := compress.ReadNum(api, c[byteNbWords:], byteNbWords, wordNbBits)
+	const sizeHeader = 3 // TODO @tabaie @gbotrel Handle this outside the circuit instead
+
+	api.AssertIsEqual(compress.ReadNum(api, c, (sizeHeader-1)*byteNbWords, wordNbBits), 0) // compressor version TODO @tabaie @gbotrel Handle this outside the circuit instead?
+	fileCompressionMode := compress.ReadNum(api, c[(sizeHeader-1)*byteNbWords:], byteNbWords, wordNbBits)
 	api.AssertIsEqual(api.Mul(fileCompressionMode, fileCompressionMode), api.Mul(fileCompressionMode, wordNbBits)) // if fcm!=0, then fcm=wordNbBits
 	decompressionNotBypassed := api.Sub(1, api.IsZero(fileCompressionMode))
 
-	c = c[2*byteNbWords:]
-	cLength = api.Sub(cLength, 2*byteNbWords)
+	c = c[sizeHeader*byteNbWords:]
+	cLength = api.Sub(cLength, sizeHeader*byteNbWords)
 
 	outTable := logderivlookup.New(api)
 	for i := range dict {
diff --git a/std/compress/lzss/snark_test.go b/std/compress/lzss/snark_test.go
index 9de006de57..f9ffcd1159 100644
--- a/std/compress/lzss/snark_test.go
+++ b/std/compress/lzss/snark_test.go
@@ -1,6 +1,9 @@
 package lzss
 
 import (
+	"os"
+	"testing"
+
 	goCompress "github.com/consensys/compress"
 	"github.com/consensys/compress/lzss"
 	"github.com/consensys/gnark-crypto/ecc"
@@ -10,8 +13,6 @@ import (
 	"github.com/consensys/gnark/test"
 	"github.com/stretchr/testify/assert"
 	"github.com/stretchr/testify/require"
-	"os"
-	"testing"
 )
 
 func Test1ZeroSnark(t *testing.T) {