diff --git a/scripts/integer-tests.sh b/scripts/integer-tests.sh
index 216d94310..9e527f992 100755
--- a/scripts/integer-tests.sh
+++ b/scripts/integer-tests.sh
@@ -28,14 +28,12 @@ if [[ "${BIG_TESTS_INSTANCE}" != TRUE ]]; then
     # block pbs are too slow for high params
     # mul_crt_4_4 is extremely flaky (~80% failure)
     # test_wopbs_bivariate_crt_wopbs_param_message generate tables that are too big at the moment
-    # same for test_wopbs_bivariate_radix_wopbs_param_message_4_carry_4
     # test_integer_smart_mul_param_message_4_carry_4 is too slow
     filter_expression=''\
 'test(/^integer::.*$/)'\
 'and not test(/.*_block_pbs(_base)?_param_message_[34]_carry_[34]$/)'\
 'and not test(~mul_crt_param_message_4_carry_4)'\
 'and not test(/.*test_wopbs_bivariate_crt_wopbs_param_message_[34]_carry_[34]$/)'\
-'and not test(/.*test_wopbs_bivariate_radix_wopbs_param_message_4_carry_4$/)'\
 'and not test(/.*test_integer_smart_mul_param_message_4_carry_4$/)'
 
     cargo ${1:+"${1}"} nextest run \
@@ -57,14 +55,12 @@ else
     # block pbs are too slow for high params
     # mul_crt_4_4 is extremely flaky (~80% failure)
     # test_wopbs_bivariate_crt_wopbs_param_message generate tables that are too big at the moment
-    # same for test_wopbs_bivariate_radix_wopbs_param_message_4_carry_4
     # test_integer_smart_mul_param_message_4_carry_4 is too slow
     filter_expression=''\
 'test(/^integer::.*$/)'\
 'and not test(/.*_block_pbs(_base)?_param_message_[34]_carry_[34]$/)'\
 'and not test(~mul_crt_param_message_4_carry_4)'\
 'and not test(/.*test_wopbs_bivariate_crt_wopbs_param_message_[34]_carry_[34]$/)'\
-'and not test(/.*test_wopbs_bivariate_radix_wopbs_param_message_4_carry_4$/)'\
 'and not test(/.*test_integer_smart_mul_param_message_4_carry_4$/)'
 
     cargo ${1:+"${1}"} nextest run \
diff --git a/tfhe/src/high_level_api/integers/server_key.rs b/tfhe/src/high_level_api/integers/server_key.rs
index a6246843c..a5d281f3e 100644
--- a/tfhe/src/high_level_api/integers/server_key.rs
+++ b/tfhe/src/high_level_api/integers/server_key.rs
@@ -120,10 +120,30 @@ impl
     ) -> crate::high_level_api::integers::server_key::RadixCiphertextDyn {
         match ct {
             RadixCiphertextDyn::Big(ct) => {
+                let mut tmp_ct: crate::integer::ciphertext::RadixCiphertextBig;
+
+                let ct = if ct.block_carries_are_empty() {
+                    ct
+                } else {
+                    tmp_ct = ct.clone();
+                    sks.full_propagate_parallelized(&mut tmp_ct);
+                    &tmp_ct
+                };
+
                 let res = wopbs_radix(self, sks, ct, f);
                 RadixCiphertextDyn::Big(res)
             }
             RadixCiphertextDyn::Small(ct) => {
+                let mut tmp_ct: crate::integer::ciphertext::RadixCiphertextSmall;
+
+                let ct = if ct.block_carries_are_empty() {
+                    ct
+                } else {
+                    tmp_ct = ct.clone();
+                    sks.full_propagate_parallelized(&mut tmp_ct);
+                    &tmp_ct
+                };
+
                 let res = wopbs_radix(self, sks, ct, f);
                 RadixCiphertextDyn::Small(res)
             }
@@ -139,10 +159,66 @@ impl
     ) -> crate::high_level_api::integers::server_key::RadixCiphertextDyn {
         match (lhs, rhs) {
             (RadixCiphertextDyn::Big(lhs), RadixCiphertextDyn::Big(rhs)) => {
+                let mut tmp_lhs: crate::integer::ciphertext::RadixCiphertextBig;
+                let mut tmp_rhs: crate::integer::ciphertext::RadixCiphertextBig;
+
+                // Clean carries to have a small wopbs to compute
+                let (lhs, rhs) =
+                    match (lhs.block_carries_are_empty(), rhs.block_carries_are_empty()) {
+                        (true, true) => (lhs, rhs),
+                        (true, false) => {
+                            tmp_rhs = rhs.clone();
+                            sks.full_propagate_parallelized(&mut tmp_rhs);
+                            (lhs, &tmp_rhs)
+                        }
+                        (false, true) => {
+                            tmp_lhs = lhs.clone();
+                            sks.full_propagate_parallelized(&mut tmp_lhs);
+                            (&tmp_lhs, rhs)
+                        }
+                        (false, false) => {
+                            tmp_lhs = lhs.clone();
+                            tmp_rhs = rhs.clone();
+                            rayon::join(
+                                || sks.full_propagate_parallelized(&mut tmp_lhs),
+                                || sks.full_propagate_parallelized(&mut tmp_rhs),
+                            );
+                            (&tmp_lhs, &tmp_rhs)
+                        }
+                    };
+
                 let res = bivariate_wopbs_radix(self, sks, lhs, rhs, f);
                 RadixCiphertextDyn::Big(res)
             }
             (RadixCiphertextDyn::Small(lhs), RadixCiphertextDyn::Small(rhs)) => {
+                let mut tmp_lhs: crate::integer::ciphertext::RadixCiphertextSmall;
+                let mut tmp_rhs: crate::integer::ciphertext::RadixCiphertextSmall;
+
+                // Clean carries to have a small wopbs to compute
+                let (lhs, rhs) =
+                    match (lhs.block_carries_are_empty(), rhs.block_carries_are_empty()) {
+                        (true, true) => (lhs, rhs),
+                        (true, false) => {
+                            tmp_rhs = rhs.clone();
+                            sks.full_propagate_parallelized(&mut tmp_rhs);
+                            (lhs, &tmp_rhs)
+                        }
+                        (false, true) => {
+                            tmp_lhs = lhs.clone();
+                            sks.full_propagate_parallelized(&mut tmp_lhs);
+                            (&tmp_lhs, rhs)
+                        }
+                        (false, false) => {
+                            tmp_lhs = lhs.clone();
+                            tmp_rhs = rhs.clone();
+                            rayon::join(
+                                || sks.full_propagate_parallelized(&mut tmp_lhs),
+                                || sks.full_propagate_parallelized(&mut tmp_rhs),
+                            );
+                            (&tmp_lhs, &tmp_rhs)
+                        }
+                    };
+
                 let res = bivariate_wopbs_radix(self, sks, lhs, rhs, f);
                 RadixCiphertextDyn::Small(res)
             }
diff --git a/tfhe/src/shortint/engine/wopbs/mod.rs b/tfhe/src/shortint/engine/wopbs/mod.rs
index 0ebd9fb00..fb476c94a 100644
--- a/tfhe/src/shortint/engine/wopbs/mod.rs
+++ b/tfhe/src/shortint/engine/wopbs/mod.rs
@@ -396,9 +396,11 @@ impl ShortintEngine {
             &mut buffer_lwe_after_ks,
         );
 
+        // The identity lut wrongly sets the max degree in the ciphertext, when in reality the
+        // degree of the ciphertext has no changed, we manage this case manually here
         Ok(CiphertextBase {
             ct: buffer_lwe_after_ks,
-            degree: ct_clean.degree,
+            degree: ct_in.degree,
             message_modulus: ct_clean.message_modulus,
             carry_modulus: ct_clean.carry_modulus,
             _order_marker: Default::default(),