diff --git a/tests/compilation/test_circuit.py b/tests/compilation/test_circuit.py
index 7587472a5..1f6e384e6 100644
--- a/tests/compilation/test_circuit.py
+++ b/tests/compilation/test_circuit.py
@@ -297,7 +297,7 @@ def test_bad_server_save(helpers):
 @pytest.mark.parametrize("p_error", [0.5, 0.1, 0.01])
 @pytest.mark.parametrize("bit_width", [10])
 @pytest.mark.parametrize("sample_size", [100_000])
-@pytest.mark.parametrize("tolerance", [0.05])
+@pytest.mark.parametrize("tolerance", [0.075])
 def test_virtual_p_error(p_error, bit_width, sample_size, tolerance, helpers):
     """
     Test virtual circuits with p_error.
diff --git a/tests/execution/test_round_bit_pattern.py b/tests/execution/test_round_bit_pattern.py
index 0d5f1f3a1..dd43f7ad0 100644
--- a/tests/execution/test_round_bit_pattern.py
+++ b/tests/execution/test_round_bit_pattern.py
@@ -162,7 +162,7 @@ def test_auto_rounding(helpers):
     # we have 4-bit inputs for this table, and we only want to use first 2-bits
     for i in range(0, 2**4, 2**2):
         # so we set every 4th entry to an 8-bit value
-        entries4[i] = np.random.randint(0, 2**8)
+        entries4[i] = np.random.randint(2**7, 2**8)
     # when this tlu is applied to a 4-bit value with 2-bit msb rounding, result will be 8-bits
     table4 = cnp.LookupTable(entries4)
     # and this is the rounder for table2, which should have lsbs_to_remove of 2