diff --git a/backends/tfhe-cuda-backend/cuda/src/integer/cmux.cuh b/backends/tfhe-cuda-backend/cuda/src/integer/cmux.cuh
index aea747c785..0325011689 100644
--- a/backends/tfhe-cuda-backend/cuda/src/integer/cmux.cuh
+++ b/backends/tfhe-cuda-backend/cuda/src/integer/cmux.cuh
@@ -14,27 +14,14 @@ __host__ void zero_out_if(cudaStream_t const *streams,
   cudaSetDevice(gpu_indexes[0]);
   auto params = mem_ptr->params;
 
-  int big_lwe_size = params.big_lwe_dimension + 1;
-
-  // Left message is shifted
-  int num_blocks = 0, num_threads = 0;
-  int num_entries = (params.big_lwe_dimension + 1);
-  getNumBlocksAndThreads(num_entries, 512, num_blocks, num_threads);
-
   // We can't use integer_radix_apply_bivariate_lookup_table_kb since the
-  // second operand is fixed
+  // second operand is not an array
   auto tmp_lwe_array_input = mem_ptr->tmp;
-  for (int i = 0; i < num_radix_blocks; i++) {
-    auto lwe_array_out_block = tmp_lwe_array_input + i * big_lwe_size;
-    auto lwe_array_input_block = lwe_array_input + i * big_lwe_size;
-
-    device_pack_bivariate_blocks<Torus>
-        <<<num_blocks, num_threads, 0, streams[0]>>>(
-            lwe_array_out_block, predicate->lwe_indexes_in,
-            lwe_array_input_block, lwe_condition, predicate->lwe_indexes_in,
-            params.big_lwe_dimension, params.message_modulus, 1);
-    check_cuda_error(cudaGetLastError());
-  }
+  pack_bivariate_blocks_with_single_block<Torus>(
+      streams, gpu_indexes, gpu_count, tmp_lwe_array_input,
+      predicate->lwe_indexes_in, lwe_array_input, lwe_condition,
+      predicate->lwe_indexes_in, params.big_lwe_dimension,
+      params.message_modulus, num_radix_blocks);
 
   integer_radix_apply_univariate_lookup_table_kb<Torus>(
       streams, gpu_indexes, gpu_count, lwe_array_out, tmp_lwe_array_input, bsks,
diff --git a/backends/tfhe-cuda-backend/cuda/src/integer/integer.cuh b/backends/tfhe-cuda-backend/cuda/src/integer/integer.cuh
index 8560b94c8d..28993ed406 100644
--- a/backends/tfhe-cuda-backend/cuda/src/integer/integer.cuh
+++ b/backends/tfhe-cuda-backend/cuda/src/integer/integer.cuh
@@ -142,8 +142,10 @@ device_pack_bivariate_blocks(Torus *lwe_array_out, Torus const *lwe_indexes_out,
     int block_id = tid / (lwe_dimension + 1);
     int coeff_id = tid % (lwe_dimension + 1);
 
-    int pos_in = lwe_indexes_in[block_id] * (lwe_dimension + 1) + coeff_id;
-    int pos_out = lwe_indexes_out[block_id] * (lwe_dimension + 1) + coeff_id;
+    const int pos_in =
+        lwe_indexes_in[block_id] * (lwe_dimension + 1) + coeff_id;
+    const int pos_out =
+        lwe_indexes_out[block_id] * (lwe_dimension + 1) + coeff_id;
     lwe_array_out[pos_out] = lwe_array_1[pos_in] * shift + lwe_array_2[pos_in];
   }
 }
@@ -172,6 +174,50 @@ pack_bivariate_blocks(cudaStream_t const *streams, uint32_t const *gpu_indexes,
   check_cuda_error(cudaGetLastError());
 }
 
+// polynomial_size threads
+template <typename Torus>
+__global__ void device_pack_bivariate_blocks_with_single_block(
+    Torus *lwe_array_out, Torus const *lwe_indexes_out,
+    Torus const *lwe_array_1, Torus const *lwe_2, Torus const *lwe_indexes_in,
+    uint32_t lwe_dimension, uint32_t shift, uint32_t num_blocks) {
+  int tid = threadIdx.x + blockIdx.x * blockDim.x;
+
+  if (tid < num_blocks * (lwe_dimension + 1)) {
+    int block_id = tid / (lwe_dimension + 1);
+    int coeff_id = tid % (lwe_dimension + 1);
+
+    const int pos_in =
+        lwe_indexes_in[block_id] * (lwe_dimension + 1) + coeff_id;
+    const int pos_out =
+        lwe_indexes_out[block_id] * (lwe_dimension + 1) + coeff_id;
+    lwe_array_out[pos_out] = lwe_array_1[pos_in] * shift + lwe_2[coeff_id];
+  }
+}
+
+/* Combine lwe_array_1 and lwe_2 so that each block m1 and lwe_2
+ *  becomes out = m1 * shift + lwe_2
+ *
+ *  This is for the special case when one of the operands is not an array
+ */
+template <typename Torus>
+__host__ void pack_bivariate_blocks_with_single_block(
+    cudaStream_t const *streams, uint32_t const *gpu_indexes,
+    uint32_t gpu_count, Torus *lwe_array_out, Torus const *lwe_indexes_out,
+    Torus const *lwe_array_1, Torus const *lwe_2, Torus const *lwe_indexes_in,
+    uint32_t lwe_dimension, uint32_t shift, uint32_t num_radix_blocks) {
+
+  cudaSetDevice(gpu_indexes[0]);
+  // Left message is shifted
+  int num_blocks = 0, num_threads = 0;
+  int num_entries = num_radix_blocks * (lwe_dimension + 1);
+  getNumBlocksAndThreads(num_entries, 512, num_blocks, num_threads);
+  device_pack_bivariate_blocks_with_single_block<Torus>
+      <<<num_blocks, num_threads, 0, streams[0]>>>(
+          lwe_array_out, lwe_indexes_out, lwe_array_1, lwe_2, lwe_indexes_in,
+          lwe_dimension, shift, num_radix_blocks);
+  check_cuda_error(cudaGetLastError());
+}
+
 template <typename Torus>
 __host__ void integer_radix_apply_univariate_lookup_table_kb(
     cudaStream_t const *streams, uint32_t const *gpu_indexes,