diff --git a/tfhe/src/integer/server_key/radix/tests.rs b/tfhe/src/integer/server_key/radix/tests.rs
index d9f3dc7f6d..af14966d28 100644
--- a/tfhe/src/integer/server_key/radix/tests.rs
+++ b/tfhe/src/integer/server_key/radix/tests.rs
@@ -60,6 +60,7 @@ create_parametrized_test!(integer_unchecked_scalar_sub);
 create_parametrized_test!(integer_unchecked_scalar_add);
 
 create_parametrized_test!(integer_unchecked_scalar_decomposition_overflow);
+create_parametrized_test!(integer_full_propagate);
 
 fn integer_encrypt_decrypt(param: ClassicPBSParameters) {
     let (cks, _) = KEY_CACHE.get_from_params(param);
@@ -1121,3 +1122,11 @@ where
     let executor = CpuFunctionExecutor::new(&ServerKey::unsigned_overflowing_sub);
     default_overflowing_sub_test(param, executor);
 }
+
+fn integer_full_propagate<P>(param: P)
+where
+    P: Into<PBSParameters>,
+{
+    let executor = CpuFunctionExecutor::new(&ServerKey::full_propagate);
+    full_propagate_test(param, executor);
+}
diff --git a/tfhe/src/integer/server_key/radix_parallel/tests_cases_unsigned.rs b/tfhe/src/integer/server_key/radix_parallel/tests_cases_unsigned.rs
index 5df2f953f6..378af62fc9 100644
--- a/tfhe/src/integer/server_key/radix_parallel/tests_cases_unsigned.rs
+++ b/tfhe/src/integer/server_key/radix_parallel/tests_cases_unsigned.rs
@@ -3096,3 +3096,159 @@ where
     });
     assert!(result.is_err(), "division by zero should panic");
 }
+
+pub(crate) fn full_propagate_test<P, T>(param: P, mut executor: T)
+where
+    P: Into<PBSParameters>,
+    T: for<'a> FunctionExecutor<&'a mut RadixCiphertext, ()>,
+{
+    let (cks, sks) = KEY_CACHE.get_from_params(param);
+
+    let cks = RadixClientKey::from((cks, NB_CTXT));
+
+    // message_modulus^vec_length
+    let modulus = cks.parameters().message_modulus().0.pow(NB_CTXT as u32) as u64;
+
+    executor.setup(&cks, sks.clone());
+
+    let block_msg_mod = cks.parameters().message_modulus().0 as u64;
+    let block_carry_mod = cks.parameters().message_modulus().0 as u64;
+    let block_total_mod = block_carry_mod * block_msg_mod;
+
+    let clear_max_value = modulus - 1;
+    for msg in 1..block_msg_mod {
+        // Here we just create a block, encrypting the max message,
+        // which means its carries are empty, and test that adding
+        // something to the first block, correctly propagates
+
+        // The first block has value block_msg_mod - 1
+        // and we will add to it a message in range [1..msg_mod-1]
+        // We still have to make sure, it won't exceed the block space
+        // (which for param_message_X_carry_X is wont)
+        if (block_msg_mod - 1) + msg >= block_total_mod {
+            continue;
+        }
+
+        let max_value = cks.encrypt(clear_max_value);
+        let rhs = cks.encrypt(msg);
+
+        let mut ct = sks.unchecked_add(&max_value, &rhs);
+        executor.execute(&mut ct);
+        let decrypted_result: u64 = cks.decrypt(&ct);
+        let expected_result = clear_max_value.wrapping_add(msg) % modulus;
+        assert_eq!(
+            decrypted_result, expected_result,
+            "Invalid full propagation result, gave ct = {clear_max_value} + {msg}, \
+            after propagation expected {expected_result}, got {decrypted_result}"
+        );
+        assert!(
+            ct.blocks
+                .iter()
+                .all(|b| b.degree.0 as u64 == block_msg_mod - 1),
+            "Invalid degree after propagation"
+        );
+    }
+
+    if block_carry_mod == block_msg_mod {
+        // This test is easier to write with this assumption
+        // which, conveniently is true for our radix type
+        //
+        // In this test, we are creating a ciphertext which is at full capacity
+        // with just enough room that allows sequential (non-parallel)
+        // propagation to work
+
+        let mut expected_result = clear_max_value;
+
+        let msg = cks.encrypt(clear_max_value);
+        let mut ct = cks.encrypt(clear_max_value);
+        while sks.is_add_possible(&ct, &msg) {
+            sks.unchecked_add_assign(&mut ct, &msg);
+            expected_result = expected_result.wrapping_add(clear_max_value) % modulus;
+        }
+        assert!(ct
+            .blocks
+            .iter()
+            .all(|b| b.degree.0 as u64 == (block_total_mod - 1) - (block_msg_mod - 1)),);
+
+        // All but the first blocks are full,
+        // So we do one more unchecked add on the first block to make it full
+        assert!(sks.is_scalar_add_possible(&ct, block_msg_mod - 1));
+        sks.unchecked_scalar_add_assign(&mut ct, block_msg_mod - 1);
+        assert_eq!(ct.blocks[0].degree.0 as u64, block_total_mod - 1);
+        expected_result = expected_result.wrapping_add(block_msg_mod - 1) % modulus;
+
+        // Do the propagation
+        executor.execute(&mut ct);
+        let decrypted_result: u64 = cks.decrypt(&ct);
+        assert_eq!(
+            decrypted_result, expected_result,
+            "Invalid full propagation result, expected {expected_result}, got {decrypted_result}"
+        );
+        assert!(
+            ct.blocks
+                .iter()
+                .all(|b| b.degree.0 as u64 == block_msg_mod - 1),
+            "Invalid degree after propagation"
+        );
+    }
+
+    {
+        // This test is written with these assumptions in mind
+        // they should hold true
+        assert!(cks.num_blocks() >= 4);
+        assert!(block_msg_mod.is_power_of_two());
+
+        // The absorber block will be set to 0
+        // All other blocks are max block msg
+        // The absorber block will 'absorb' carry propagation
+        let absorber_block_index = 2;
+
+        let mut ct = cks.encrypt(clear_max_value);
+        ct.blocks[absorber_block_index] = cks.encrypt_one_block(0); // use cks to have noise
+
+        let block_mask = block_msg_mod - 1;
+        let num_bits_in_msg = block_msg_mod.ilog2();
+        // Its 00..11..00 (only bits of the absorber block set to 1
+        let absorber_block_mask = block_mask << (absorber_block_index as u32 * num_bits_in_msg);
+        let mask = u64::MAX ^ absorber_block_mask;
+        // Initial value has all its bits set to one (bits that are in modulus)
+        // except for the bits in the absorber block which are 0s
+        let initial_value = clear_max_value & mask;
+
+        let to_add = cks.encrypt(block_msg_mod - 1);
+        sks.unchecked_add_assign(&mut ct, &to_add);
+        let expected_result = initial_value.wrapping_add(block_msg_mod - 1) % modulus;
+        // Do the propagation
+        executor.execute(&mut ct);
+        let decrypted_result: u64 = cks.decrypt(&ct);
+        assert_eq!(
+            decrypted_result, expected_result,
+            "Invalid full propagation result, expected {expected_result}, got {decrypted_result}"
+        );
+        assert!(
+            ct.blocks
+                .iter()
+                .all(|b| b.degree.0 as u64 == block_msg_mod - 1),
+            "Invalid degree after propagation"
+        );
+
+        // Take the initial value, but remove any bits below absober block
+        // as the bits below will have changed, but bits above will not.
+        let mut expected_built_by_hand =
+            initial_value & (u64::MAX << ((absorber_block_index + 1) as u32 * num_bits_in_msg));
+        // The first block generated a carry,
+        // but also results in a non zero block.
+        //
+        // The carry gets propagated by other blocks
+        // until it hits the absorber block, which takes the value of the carry
+        // (1) as its new value. Blocks that propagated the carry will have as new value
+        // 0 as for these block we did: ((block_msg_mod - 1  + 1) % block_msg_modulus) == 0
+        // and carry = ((block_msg_mod - 1  + 1) / block_msg_modulus) == 1
+        //
+        // Set the value of first block
+        expected_built_by_hand |= (2 * (block_msg_mod - 1)) % block_msg_mod;;
+        // Set the value of the absorbed block
+        expected_built_by_hand |= 1 << (absorber_block_index as u32 * num_bits_in_msg);
+        assert_eq!(expected_result, expected_built_by_hand);
+    }
+}
diff --git a/tfhe/src/integer/server_key/radix_parallel/tests_unsigned.rs b/tfhe/src/integer/server_key/radix_parallel/tests_unsigned.rs
index aa1ebf6f3c..7dd6fdebf0 100644
--- a/tfhe/src/integer/server_key/radix_parallel/tests_unsigned.rs
+++ b/tfhe/src/integer/server_key/radix_parallel/tests_unsigned.rs
@@ -238,6 +238,7 @@ create_parametrized_test!(integer_unchecked_add);
 create_parametrized_test!(integer_unchecked_mul);
 
 create_parametrized_test!(integer_unchecked_add_assign);
+create_parametrized_test!(integer_full_propagate);
 
 /// The function executor for cpu server key
 ///
@@ -278,6 +279,21 @@ where
     }
 }
 
+/// Unary assign fn
+impl<'a, F> FunctionExecutor<&'a mut RadixCiphertext, ()> for CpuFunctionExecutor<F>
+where
+    F: Fn(&ServerKey, &'a mut RadixCiphertext),
+{
+    fn setup(&mut self, _cks: &RadixClientKey, sks: ServerKey) {
+        self.sks = Some(sks)
+    }
+
+    fn execute(&mut self, input: &'a mut RadixCiphertext) {
+        let sks = self.sks.as_ref().expect("setup was not properly called");
+        (self.func)(sks, input)
+    }
+}
+
 impl<'a, F> FunctionExecutor<&'a mut RadixCiphertext, RadixCiphertext> for CpuFunctionExecutor<F>
 where
     F: Fn(&ServerKey, &mut RadixCiphertext) -> RadixCiphertext,
@@ -1076,3 +1092,11 @@ where
     let output: u64 = client_key.decrypt(&ct_3);
     assert_eq!(output, (msg2 + msg1) % (modulus));
 }
+
+fn integer_full_propagate<P>(param: P)
+where
+    P: Into<PBSParameters>,
+{
+    let executor = CpuFunctionExecutor::new(&ServerKey::full_propagate_parallelized);
+    full_propagate_test(param, executor);
+}