diff --git a/projects/proquint/test/python/test_examples.py b/projects/proquint/test/python/test_examples.py
index 486c2d3..8bf4444 100644
--- a/projects/proquint/test/python/test_examples.py
+++ b/projects/proquint/test/python/test_examples.py
@@ -55,3 +55,8 @@ def test_encode_examples(val, width, qint):
     assert (
         encoded_qint == qint
     ), f"did not encode {val} to {qint}; got {encoded_qint} ({decoded_val})"
+
+# Previously failed test values -
+# 4294967296
+# 18446744073709551616
+# 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096
diff --git a/projects/proquint/test/python/test_hypothesis.py b/projects/proquint/test/python/test_hypothesis.py
index a7f0318..5650c06 100644
--- a/projects/proquint/test/python/test_hypothesis.py
+++ b/projects/proquint/test/python/test_hypothesis.py
@@ -5,21 +5,22 @@ from hypothesis.strategies import integers
 import proquint
 
 
-@given(integers(min_value=0, max_value=1 << 16))
-def test_round_trip_16(val):
-    assert proquint.Proquint.decode(proquint.Proquint.encode(val, 16)) == val
+def test_round_trip_16():
+    for val in range(0, 1<<16):
+        assert proquint.Proquint.decode(proquint.Proquint.encode(val, 16)) == val
 
 
-@given(integers(min_value=0, max_value=1 << 32))
+@given(integers(min_value=1<<16, max_value=1 << 32 - 1))
 def test_round_trip_32(val):
     assert proquint.Proquint.decode(proquint.Proquint.encode(val, 32)) == val
 
 
-@given(integers(min_value=0, max_value=1 << 64))
+@given(integers(min_value=1<<16, max_value=1 << 64 - 1))
 def test_round_trip_64(val):
     assert proquint.Proquint.decode(proquint.Proquint.encode(val, 64)) == val
 
 
-@given(integers(min_value=0, max_value=1 << 512))
+@given(integers(min_value=1<<16, max_value=1 << 512 - 1))
 def test_round_trip_512(val):
     assert proquint.Proquint.decode(proquint.Proquint.encode(val, 512)) == val
+