diff --git a/pubkey_test.go b/pubkey_test.go
index 581cdc41..05ada643 100644
--- a/pubkey_test.go
+++ b/pubkey_test.go
@@ -139,6 +139,58 @@ var pubKeyTests = []pubKeyTest{
 		key:     []byte{0x05},
 		isValid: false,
 	},
+	pubKeyTest{
+		name: "X == P",
+		key: []byte{0x04, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+			0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+			0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+			0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFC, 0x2F, 0xb2, 0xe0,
+			0xea, 0xdd, 0xfb, 0x84, 0xcc, 0xf9, 0x74, 0x44, 0x64,
+			0xf8, 0x2e, 0x16, 0x0b, 0xfa, 0x9b, 0x8b, 0x64, 0xf9,
+			0xd4, 0xc0, 0x3f, 0x99, 0x9b, 0x86, 0x43, 0xf6, 0x56,
+			0xb4, 0x12, 0xa3,
+		},
+		isValid: false,
+	},
+	pubKeyTest{
+		name: "X > P",
+		key: []byte{0x04, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+			0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+			0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+			0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFD, 0x2F, 0xb2, 0xe0,
+			0xea, 0xdd, 0xfb, 0x84, 0xcc, 0xf9, 0x74, 0x44, 0x64,
+			0xf8, 0x2e, 0x16, 0x0b, 0xfa, 0x9b, 0x8b, 0x64, 0xf9,
+			0xd4, 0xc0, 0x3f, 0x99, 0x9b, 0x86, 0x43, 0xf6, 0x56,
+			0xb4, 0x12, 0xa3,
+		},
+		isValid: false,
+	},
+	pubKeyTest{
+		name: "Y == P",
+		key: []byte{0x04, 0x11, 0xdb, 0x93, 0xe1, 0xdc, 0xdb, 0x8a,
+			0x01, 0x6b, 0x49, 0x84, 0x0f, 0x8c, 0x53, 0xbc, 0x1e,
+			0xb6, 0x8a, 0x38, 0x2e, 0x97, 0xb1, 0x48, 0x2e, 0xca,
+			0xd7, 0xb1, 0x48, 0xa6, 0x90, 0x9a, 0x5c, 0xFF, 0xFF,
+			0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+			0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+			0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF,
+			0xFF, 0xFC, 0x2F,
+		},
+		isValid: false,
+	},
+	pubKeyTest{
+		name: "Y > P",
+		key: []byte{0x04, 0x11, 0xdb, 0x93, 0xe1, 0xdc, 0xdb, 0x8a,
+			0x01, 0x6b, 0x49, 0x84, 0x0f, 0x8c, 0x53, 0xbc, 0x1e,
+			0xb6, 0x8a, 0x38, 0x2e, 0x97, 0xb1, 0x48, 0x2e, 0xca,
+			0xd7, 0xb1, 0x48, 0xa6, 0x90, 0x9a, 0x5c, 0xFF, 0xFF,
+			0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+			0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+			0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF,
+			0xFF, 0xFD, 0x2F,
+		},
+		isValid: false,
+	},
 }
 
 func TestPubKeys(t *testing.T) {
diff --git a/test_coverage.txt b/test_coverage.txt
index fc212146..bc483a57 100644
--- a/test_coverage.txt
+++ b/test_coverage.txt
@@ -11,10 +11,10 @@ github.com/conformal/btcec/btcec.go	 KoblitzCurve.Params		 100.00% (1/1)
 github.com/conformal/btcec/btcec.go	 KoblitzCurve.ScalarBaseMult	 100.00% (1/1)
 github.com/conformal/btcec/btcec.go	 initAll			 100.00% (1/1)
 github.com/conformal/btcec/pubkey.go	 isOdd				 100.00% (1/1)
+github.com/conformal/btcec/pubkey.go	 ParsePubKey			 96.88% (31/32)
 github.com/conformal/btcec/btcec.go	 KoblitzCurve.addJacobian	 91.67% (55/60)
-github.com/conformal/btcec/pubkey.go	 ParsePubKey			 90.62% (29/32)
 github.com/conformal/btcec/btcec.go	 KoblitzCurve.affineFromJacobian 90.00% (9/10)
 github.com/conformal/btcec/signature.go	 ParseSignature			 0.00% (0/41)
 github.com/conformal/btcec/btcec.go	 KoblitzCurve.Double		 0.00% (0/2)
-github.com/conformal/btcec		 ------------------------------- 74.63% (153/205)
+github.com/conformal/btcec		 ------------------------------- 75.61% (155/205)