diff --git a/src/isbn.zig b/src/isbn.zig
index e49f2ab..57af202 100644
--- a/src/isbn.zig
+++ b/src/isbn.zig
@@ -52,6 +52,9 @@ pub const ISBN = union(enum) {
                 return tmp;
             },
             13 => {
+                // 'X' is only valid as the check digit of an ISBN-10; the
+                // scan loop can only have accepted it at index 9.
+                if (buf[9] == 'X') return error.ParseError;
                 var tmp: ISBN = .{
                     .@"13" = undefined,
                 };
@@ -226,6 +229,53 @@ test "13 1" {
     try std.testing.expectEqual('7', c);
 }
 
+test "13 2" {
+    const x: ISBN = try .parse("979-10-90636-07-1");
+    try std.testing.expect(x == .@"13");
+    try std.testing.expectEqualSlices(u8, "9791090636071", &x.@"13");
+    const c = x.computeCheckDigit();
+    try std.testing.expectEqual('1', c);
+}
+
+test "10 check digit 0" {
+    const x: ISBN = try .parse("0-00-000000-0");
+    try std.testing.expect(x == .@"10");
+    const c = x.computeCheckDigit();
+    try std.testing.expectEqual('0', c);
+}
+
+test "13 check digit 0" {
+    const x: ISBN = try .parse("978-0-00-000020-0");
+    try std.testing.expect(x == .@"13");
+    const c = x.computeCheckDigit();
+    try std.testing.expectEqual('0', c);
+}
+
+test "parse rejects malformed input" {
+    try std.testing.expectError(error.ParseError, ISBN.parse(""));
+    try std.testing.expectError(error.ParseError, ISBN.parse("---"));
+    try std.testing.expectError(error.ParseError, ISBN.parse("0-306-40615")); // 9 digits
+    try std.testing.expectError(error.ParseError, ISBN.parse("0-306-40615-22")); // 11 digits
+    try std.testing.expectError(error.ParseError, ISBN.parse("978-0-306-40615")); // 12 digits
+    try std.testing.expectError(error.ParseError, ISBN.parse("978-0-306-40615-72")); // 14 digits
+    try std.testing.expectError(error.ParseError, ISBN.parse("0-306-4X615-2")); // X in wrong position
+    try std.testing.expectError(error.ParseError, ISBN.parse("0-306-40615-A")); // invalid character
+    try std.testing.expectError(error.ParseError, ISBN.parse("0 306 40615 2")); // space separator
+}
+
+test "parse rejects X in an ISBN-13" {
+    // 'X' - '0' is 40, which at position 9 (weight 3) contributes
+    // 120 = 0 (mod 10), so this string is checksum-valid and must be
+    // rejected before the check-digit comparison.
+    try std.testing.expectError(error.ParseError, ISBN.parse("978-0-306-40X15-5"));
+}
+
+test "parse rejects invalid check digits" {
+    try std.testing.expectError(error.InvalidCheckDigit, ISBN.parse("0-306-40615-3"));
+    try std.testing.expectError(error.InvalidCheckDigit, ISBN.parse("0-8044-2957-4")); // expects X
+    try std.testing.expectError(error.InvalidCheckDigit, ISBN.parse("978-0-306-40615-8"));
+}
+
 test "upgrade and eql" {
     const ten: ISBN = try .parse("0-306-40615-2");
     const thirteen: ISBN = try .parse("978-0-306-40615-7");