diff --git a/Makefile b/Makefile
index 95b191fd1..cd901105f 100644
--- a/Makefile
+++ b/Makefile
@@ -16,6 +16,7 @@ GEN_KEY_CACHE_COVERAGE_ONLY?=FALSE
 PARSE_INTEGER_BENCH_CSV_FILE?=tfhe_rs_integer_benches.csv
 FAST_TESTS?=FALSE
 FAST_BENCH?=FALSE
+NIGHTLY_TESTS?=FALSE
 BENCH_OP_FLAVOR?=DEFAULT
 NODE_VERSION=22
 FORWARD_COMPAT?=OFF
@@ -481,6 +482,7 @@ test_integer_gpu: install_rs_build_toolchain
 test_integer_gpu_ci: install_rs_check_toolchain install_cargo_nextest
 	BIG_TESTS_INSTANCE="$(BIG_TESTS_INSTANCE)" \
 	FAST_TESTS="$(FAST_TESTS)" \
+	NIGHTLY_TESTS="$(NIGHTLY_TESTS)" \
 		./scripts/integer-tests.sh --rust-toolchain $(CARGO_RS_CHECK_TOOLCHAIN) \
 		--cargo-profile "$(CARGO_PROFILE)" --backend "gpu" \
 		--tfhe-package "$(TFHE_SPEC)"
@@ -489,6 +491,7 @@ test_integer_gpu_ci: install_rs_check_toolchain install_cargo_nextest
 test_unsigned_integer_gpu_ci: install_rs_check_toolchain install_cargo_nextest
 	BIG_TESTS_INSTANCE="$(BIG_TESTS_INSTANCE)" \
 	FAST_TESTS="$(FAST_TESTS)" \
+	NIGHTLY_TESTS="$(NIGHTLY_TESTS)" \
 		./scripts/integer-tests.sh --rust-toolchain $(CARGO_RS_CHECK_TOOLCHAIN) \
 		--cargo-profile "$(CARGO_PROFILE)" --backend "gpu" \
 		--unsigned-only --tfhe-package "$(TFHE_SPEC)"
@@ -497,6 +500,7 @@ test_unsigned_integer_gpu_ci: install_rs_check_toolchain install_cargo_nextest
 test_signed_integer_gpu_ci: install_rs_check_toolchain install_cargo_nextest
 	BIG_TESTS_INSTANCE="$(BIG_TESTS_INSTANCE)" \
 	FAST_TESTS="$(FAST_TESTS)" \
+	NIGHTLY_TESTS="$(NIGHTLY_TESTS)" \
 		./scripts/integer-tests.sh --rust-toolchain $(CARGO_RS_CHECK_TOOLCHAIN) \
 		--cargo-profile "$(CARGO_PROFILE)" --backend "gpu" \
 		--signed-only --tfhe-package "$(TFHE_SPEC)"
@@ -505,6 +509,7 @@ test_signed_integer_gpu_ci: install_rs_check_toolchain install_cargo_nextest
 test_integer_multi_bit_gpu_ci: install_rs_check_toolchain install_cargo_nextest
 	BIG_TESTS_INSTANCE="$(BIG_TESTS_INSTANCE)" \
 	FAST_TESTS="$(FAST_TESTS)" \
+	NIGHTLY_TESTS="$(NIGHTLY_TESTS)" \
 		./scripts/integer-tests.sh --rust-toolchain $(CARGO_RS_CHECK_TOOLCHAIN) \
 		--cargo-profile "$(CARGO_PROFILE)" --multi-bit --backend "gpu" \
 		--tfhe-package "$(TFHE_SPEC)"
@@ -513,6 +518,7 @@ test_integer_multi_bit_gpu_ci: install_rs_check_toolchain install_cargo_nextest
 test_unsigned_integer_multi_bit_gpu_ci: install_rs_check_toolchain install_cargo_nextest
 	BIG_TESTS_INSTANCE="$(BIG_TESTS_INSTANCE)" \
 	FAST_TESTS="$(FAST_TESTS)" \
+	NIGHTLY_TESTS="$(NIGHTLY_TESTS)" \
 		./scripts/integer-tests.sh --rust-toolchain $(CARGO_RS_CHECK_TOOLCHAIN) \
 		--cargo-profile "$(CARGO_PROFILE)" --multi-bit --backend "gpu" \
 		--unsigned-only --tfhe-package "$(TFHE_SPEC)"
@@ -521,6 +527,7 @@ test_unsigned_integer_multi_bit_gpu_ci: install_rs_check_toolchain install_cargo
 test_signed_integer_multi_bit_gpu_ci: install_rs_check_toolchain install_cargo_nextest
 	BIG_TESTS_INSTANCE="$(BIG_TESTS_INSTANCE)" \
 	FAST_TESTS="$(FAST_TESTS)" \
+	NIGHTLY_TESTS="$(NIGHTLY_TESTS)" \
 		./scripts/integer-tests.sh --rust-toolchain $(CARGO_RS_CHECK_TOOLCHAIN) \
 		--cargo-profile "$(CARGO_PROFILE)" --multi-bit --backend "gpu" \
 		--signed-only --tfhe-package "$(TFHE_SPEC)"
@@ -587,6 +594,7 @@ test_shortint_cov: install_rs_check_toolchain install_tarpaulin
 test_integer_ci: install_rs_check_toolchain install_cargo_nextest
 	BIG_TESTS_INSTANCE="$(BIG_TESTS_INSTANCE)" \
 	FAST_TESTS="$(FAST_TESTS)" \
+	NIGHTLY_TESTS="$(NIGHTLY_TESTS)" \
 		./scripts/integer-tests.sh --rust-toolchain $(CARGO_RS_CHECK_TOOLCHAIN) \
 		--cargo-profile "$(CARGO_PROFILE)" --avx512-support "$(AVX512_SUPPORT)" \
 		--tfhe-package "$(TFHE_SPEC)"
@@ -595,6 +603,7 @@ test_integer_ci: install_rs_check_toolchain install_cargo_nextest
 test_unsigned_integer_ci: install_rs_check_toolchain install_cargo_nextest
 	BIG_TESTS_INSTANCE="$(BIG_TESTS_INSTANCE)" \
 	FAST_TESTS="$(FAST_TESTS)" \
+	NIGHTLY_TESTS="$(NIGHTLY_TESTS)" \
 		./scripts/integer-tests.sh --rust-toolchain $(CARGO_RS_CHECK_TOOLCHAIN) \
 		--cargo-profile "$(CARGO_PROFILE)" --avx512-support "$(AVX512_SUPPORT)" \
 		--unsigned-only --tfhe-package "$(TFHE_SPEC)"
@@ -603,6 +612,7 @@ test_unsigned_integer_ci: install_rs_check_toolchain install_cargo_nextest
 test_signed_integer_ci: install_rs_check_toolchain install_cargo_nextest
 	BIG_TESTS_INSTANCE="$(BIG_TESTS_INSTANCE)" \
 	FAST_TESTS="$(FAST_TESTS)" \
+	NIGHTLY_TESTS="$(NIGHTLY_TESTS)" \
 		./scripts/integer-tests.sh --rust-toolchain $(CARGO_RS_CHECK_TOOLCHAIN) \
 		--cargo-profile "$(CARGO_PROFILE)" --avx512-support "$(AVX512_SUPPORT)" \
 		--signed-only --tfhe-package "$(TFHE_SPEC)"
@@ -611,6 +621,7 @@ test_signed_integer_ci: install_rs_check_toolchain install_cargo_nextest
 test_integer_multi_bit_ci: install_rs_check_toolchain install_cargo_nextest
 	BIG_TESTS_INSTANCE="$(BIG_TESTS_INSTANCE)" \
 	FAST_TESTS="$(FAST_TESTS)" \
+	NIGHTLY_TESTS="$(NIGHTLY_TESTS)" \
 		./scripts/integer-tests.sh --rust-toolchain $(CARGO_RS_CHECK_TOOLCHAIN) \
 		--cargo-profile "$(CARGO_PROFILE)" --multi-bit --avx512-support "$(AVX512_SUPPORT)" \
 		--tfhe-package "$(TFHE_SPEC)"
@@ -619,6 +630,7 @@ test_integer_multi_bit_ci: install_rs_check_toolchain install_cargo_nextest
 test_unsigned_integer_multi_bit_ci: install_rs_check_toolchain install_cargo_nextest
 	BIG_TESTS_INSTANCE="$(BIG_TESTS_INSTANCE)" \
 	FAST_TESTS="$(FAST_TESTS)" \
+	NIGHTLY_TESTS="$(NIGHTLY_TESTS)" \
 		./scripts/integer-tests.sh --rust-toolchain $(CARGO_RS_CHECK_TOOLCHAIN) \
 		--cargo-profile "$(CARGO_PROFILE)" --multi-bit --avx512-support "$(AVX512_SUPPORT)" \
 		--unsigned-only --tfhe-package "$(TFHE_SPEC)"
@@ -627,6 +639,7 @@ test_unsigned_integer_multi_bit_ci: install_rs_check_toolchain install_cargo_nex
 test_signed_integer_multi_bit_ci: install_rs_check_toolchain install_cargo_nextest
 	BIG_TESTS_INSTANCE="$(BIG_TESTS_INSTANCE)" \
 	FAST_TESTS="$(FAST_TESTS)" \
+	NIGHTLY_TESTS="$(NIGHTLY_TESTS)" \
 		./scripts/integer-tests.sh --rust-toolchain $(CARGO_RS_CHECK_TOOLCHAIN) \
 		--cargo-profile "$(CARGO_PROFILE)" --multi-bit --avx512-support "$(AVX512_SUPPORT)" \
 		--signed-only --tfhe-package "$(TFHE_SPEC)"
diff --git a/scripts/integer-tests.sh b/scripts/integer-tests.sh
index 5477e6014..98258edae 100755
--- a/scripts/integer-tests.sh
+++ b/scripts/integer-tests.sh
@@ -21,6 +21,7 @@ RUST_TOOLCHAIN="+stable"
 multi_bit_argument=
 sign_argument=
 fast_tests_argument=
+nightly_tests_argument=
 no_big_params_argument=
 cargo_profile="release"
 backend="cpu"
@@ -90,6 +91,10 @@ if [[ "${FAST_TESTS}" == TRUE ]]; then
     fast_tests_argument=--fast-tests
 fi
 
+if [[ "${NIGHTLY_TESTS}" == TRUE ]]; then
+    nightly_tests_argument=--nightly-tests
+fi
+
 if [[ "${NO_BIG_PARAMS}" == TRUE ]]; then
     no_big_params_argument=--no-big-params
 fi
@@ -127,14 +132,18 @@ if [[ "${backend}" == "gpu" ]]; then
     test_threads=6
 fi
 
-filter_expression=$(/usr/bin/python3 scripts/test_filtering.py --layer integer --backend "${backend}" ${fast_tests_argument} ${multi_bit_argument} ${sign_argument} ${no_big_params_argument})
+filter_expression=$(/usr/bin/python3 scripts/test_filtering.py --layer integer --backend "${backend}" ${fast_tests_argument} ${nightly_tests_argument} ${multi_bit_argument} ${sign_argument} ${no_big_params_argument})
 
 if [[ "${FAST_TESTS}" == "TRUE" ]]; then
-    echo "Running 'fast' test set'"
+    echo "Running 'fast' test set"
 else
     echo "Running 'slow' test set"
 fi
 
+if [[ "${NIGHTLY_TESTS}" == "TRUE" ]]; then
+    echo "Running 'nightly' test set"
+fi
+
 cargo "${RUST_TOOLCHAIN}" nextest run \
     --tests \
     --cargo-profile "${cargo_profile}" \
diff --git a/scripts/test_filtering.py b/scripts/test_filtering.py
index 43d741076..b9fdbce04 100644
--- a/scripts/test_filtering.py
+++ b/scripts/test_filtering.py
@@ -2,6 +2,7 @@
 Script that generates a cargo-nextest filter as an output.
 The string result can be directly injected into a nextest command.
 """
+
 import argparse
 
 parser = argparse.ArgumentParser(allow_abbrev=False)
@@ -25,6 +26,12 @@ parser.add_argument(
     action="store_true",
     help="Run only a small subset of test suite",
 )
+parser.add_argument(
+    "--nightly-tests",
+    dest="nightly_tests",
+    action="store_true",
+    help="Run only a subset of test suite",
+)
 parser.add_argument(
     "--big-instance",
     dest="big_instance",
@@ -87,6 +94,7 @@ EXCLUDED_BIG_PARAMETERS = [
     "/.*_param_message_4_carry_4_ks_pbs$/",
 ]
 
+
 def filter_integer_tests(input_args):
     multi_bit_filter = "_multi_bit" if input_args.multi_bit else ""
     backend_filter = ""
@@ -109,11 +117,20 @@ def filter_integer_tests(input_args):
         for pattern in EXCLUDED_BIG_PARAMETERS:
             filter_expression.append(f"not test({pattern})")
 
-    if input_args.fast_tests:
-        # Test only fast default operations with only one set of parameters
-        param_group = "_group_2" if input_args.multi_bit else ""
+    if input_args.fast_tests and input_args.nightly_tests:
         filter_expression.append(
-            f"test(/.*_default_.*?_param{multi_bit_filter}_message_2_carry_2{param_group}_.*/)"
+            f"test(/.*_default_.*?_param{multi_bit_filter}_message_[2-3]_carry_[2-3]_.*/)"
+        )
+    elif input_args.fast_tests:
+        # Test only fast default operations with only one set of parameters
+        filter_expression.append(
+            f"test(/.*_default_.*?_param{multi_bit_filter}_message_2_carry_2_.*/)"
+        )
+    elif input_args.nightly_tests:
+        # Test only fast default operations with only one set of parameters
+        # This subset would run slower than fast_tests hence the use of nightly_tests
+        filter_expression.append(
+            f"test(/.*_default_.*?_param{multi_bit_filter}_message_3_carry_3_.*/)"
         )
 
     excluded_tests = (