diff --git a/src/ecdsa/test_ellipticcurve.py b/src/ecdsa/test_ellipticcurve.py
index 31f9e0d8..864cf108 100644
--- a/src/ecdsa/test_ellipticcurve.py
+++ b/src/ecdsa/test_ellipticcurve.py
@@ -83,6 +83,11 @@ def test_inequality_curves(self):
         c192 = CurveFp(p, -3, b)
         self.assertNotEqual(self.c_23, c192)
 
+    def test_inequality_curves_by_b_only(self):
+        a = CurveFp(23, 1, 0)
+        b = CurveFp(23, 1, 1)
+        self.assertNotEqual(a, b)
+
     def test_usability_in_a_hashed_collection_curves(self):
         {self.c_23: None}
 
diff --git a/src/ecdsa/test_pyecdsa.py b/src/ecdsa/test_pyecdsa.py
index 0a4ed8af..6c0266e8 100644
--- a/src/ecdsa/test_pyecdsa.py
+++ b/src/ecdsa/test_pyecdsa.py
@@ -856,6 +856,22 @@ def test_hybrid_decoding_with_blocked_format(self):
 
         self.assertIn("Invalid X9.62 encoding", str(exp.exception))
 
+    def test_hybrid_decoding_with_inconsistent_encoding_and_no_validation(self):
+        sk = SigningKey.from_secret_exponent(123456789)
+        vk = sk.verifying_key
+
+        enc = vk.to_string("hybrid")
+        self.assertEqual(enc[:1], b'\x06')
+        enc = b'\x07' + enc[1:]
+
+        b = VerifyingKey.from_string(
+            enc,
+            valid_encodings=("hybrid",),
+            validate_point=False
+        )
+
+        self.assertEqual(vk, b)
+
     def test_compressed_decoding_with_blocked_format(self):
         enc = (
             b"\x02"
@@ -898,6 +914,17 @@ def test_decoding_with_inconsistent_hybrid(self):
         with self.assertRaises(MalformedPointError):
             VerifyingKey.from_string(b"\x07" + enc)
 
+    def test_decoding_with_inconsistent_hybrid_odd_point(self):
+        sk = SigningKey.from_secret_exponent(123456791)
+        vk = sk.verifying_key
+
+        enc = vk.to_string("hybrid")
+        self.assertEqual(enc[:1], b'\x07')
+        enc = b'\x06' + enc[1:]
+
+        with self.assertRaises(MalformedPointError):
+            b = VerifyingKey.from_string(enc, valid_encodings=("hybrid",))
+
     def test_decoding_with_point_not_on_curve(self):
         enc = (
             b"\x0c\xe0\x1d\xe0d\x1c\x8eS\x8a\xc0\x9eK\xa8x !\xd5\xc2\xc3"