diff --git a/concrete/common/mlir/utils.py b/concrete/common/mlir/utils.py
index c464d9d43..b6297eef8 100644
--- a/concrete/common/mlir/utils.py
+++ b/concrete/common/mlir/utils.py
@@ -115,8 +115,14 @@ def check_node_compatibility_with_mlir(
 
     if is_output:
         for out in outputs:
-            if not value_is_unsigned_integer(out):
-                return "only unsigned integer outputs are supported"
+            # For signed values and waiting for a real fix (#845): what is returned by the compiler
+            # is not the (possibly negative) result r, but the always-positive (r mod 2**t), where t
+            # is the bitwidth of r
+
+            # We currently can't fail on the following assert, but let it for possible changes in
+            # the future
+            if not value_is_integer(out):
+                return "only integer outputs are supported"  # pragma: no cover
     else:
         for out in outputs:
             # We currently can't fail on the following assert, but let it for possible changes in
diff --git a/tests/numpy/test_compile.py b/tests/numpy/test_compile.py
index 40be43ddb..4ef224683 100644
--- a/tests/numpy/test_compile.py
+++ b/tests/numpy/test_compile.py
@@ -1033,24 +1033,6 @@ def test_compile_function_with_direct_tlu_overflow(default_compilation_configura
 @pytest.mark.parametrize(
     "function,parameters,inputset,match",
     [
-        pytest.param(
-            lambda x: 1 - x,
-            {"x": EncryptedScalar(Integer(3, is_signed=False))},
-            [(i,) for i in range(8)],
-            (
-                """
-
-function you are trying to compile isn't supported for MLIR lowering
-
-%0 = 1                  # ClearScalar<uint1>
-%1 = x                  # EncryptedScalar<uint3>
-%2 = sub(%0, %1)        # EncryptedScalar<int4>
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ only unsigned integer outputs are supported
-return %2
-
-                """.strip()  # noqa: E501
-            ),
-        ),
         pytest.param(
             lambda x, y: numpy.dot(x, y),
             {
@@ -1476,44 +1458,6 @@ return %2
     )
 
 
-def test_failure_for_signed_output(default_compilation_configuration):
-    """Test that we don't accept signed output"""
-    function = lambda x: x + (-3)  # noqa: E731
-    input_ranges = ((0, 10),)
-    list_of_arg_names = ["x"]
-
-    def data_gen(args):
-        for prod in itertools.product(*args):
-            yield prod
-
-    function_parameters = {
-        arg_name: EncryptedScalar(Integer(64, False)) for arg_name in list_of_arg_names
-    }
-
-    with pytest.raises(RuntimeError) as excinfo:
-        compile_numpy_function(
-            function,
-            function_parameters,
-            data_gen(tuple(range(x[0], x[1] + 1) for x in input_ranges)),
-            default_compilation_configuration,
-        )
-
-    assert (
-        str(excinfo.value)
-        == """
-
-function you are trying to compile isn't supported for MLIR lowering
-
-%0 = x                  # EncryptedScalar<uint4>
-%1 = -3                 # ClearScalar<int3>
-%2 = add(%0, %1)        # EncryptedScalar<int4>
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ only unsigned integer outputs are supported
-return %2
-
-""".strip()  # noqa: E501 # pylint: disable=line-too-long
-    )
-
-
 def test_compile_with_random_inputset(default_compilation_configuration):
     """Test function for compile with random input set"""
 
@@ -1649,3 +1593,41 @@ def test_compile_and_run_correctness_with_negative_values(
 
     args = [random.randint(low, high) for (low, high) in input_ranges]
     assert compiler_engine.run(*args) == function(*args)
+
+
+def check_equality_modulo(a, b, modulus):
+    """Check that (a mod modulus) == (b mod modulus)"""
+    return (a % modulus) == (b % modulus)
+
+
+@pytest.mark.parametrize(
+    "function,input_ranges,list_of_arg_names,modulus",
+    [
+        pytest.param(lambda x: x + (-20), ((0, 10),), ["x"], 128),
+        pytest.param(lambda x: 10 + x * (-3), ((0, 20),), ["x"], 128),
+    ],
+)
+def test_compile_and_run_correctness_with_negative_results(
+    function, input_ranges, list_of_arg_names, modulus, default_compilation_configuration
+):
+    """Test correctness of computations when the result is possibly negative: until #845 is fixed,
+    results are currently only correct modulo a power of 2 (given by `modulus` parameter). Eg,
+    instead of returning -3, the execution may return -3 mod 128 = 125."""
+
+    def data_gen(args):
+        for prod in itertools.product(*args):
+            yield prod
+
+    function_parameters = {
+        arg_name: EncryptedScalar(Integer(64, False)) for arg_name in list_of_arg_names
+    }
+
+    compiler_engine = compile_numpy_function(
+        function,
+        function_parameters,
+        data_gen(tuple(range(x[0], x[1] + 1) for x in input_ranges)),
+        default_compilation_configuration,
+    )
+
+    args = [random.randint(low, high) for (low, high) in input_ranges]
+    assert check_equality_modulo(compiler_engine.run(*args), function(*args), modulus)