diff --git a/aes_test.go b/aes_test.go
index 142ac878..71162e87 100644
--- a/aes_test.go
+++ b/aes_test.go
@@ -155,12 +155,12 @@ func TestSealAndOpenTLS(t *testing.T) {
 	key := []byte("D249BF6DEC97B1EBD69BC4D6B3A3C49D")
 	tests := []struct {
 		name string
-		new  func(c cipher.Block) (cipher.AEAD, error)
+		tls  string
 		mask func(n *[12]byte)
 	}{
-		{"1.2", openssl.NewGCMTLS, nil},
-		{"1.3", openssl.NewGCMTLS13, nil},
-		{"1.3_masked", openssl.NewGCMTLS13, func(n *[12]byte) {
+		{"1.2", "1.2", nil},
+		{"1.3", "1.3", nil},
+		{"1.3_masked", "1.3", func(n *[12]byte) {
 			// Arbitrary mask in the high bits.
 			n[9] ^= 0x42
 			// Mask the very first bit. This makes sure that if Seal doesn't
@@ -175,7 +175,13 @@ func TestSealAndOpenTLS(t *testing.T) {
 			if err != nil {
 				t.Fatal(err)
 			}
-			gcm, err := tt.new(ci)
+			var gcm cipher.AEAD
+			switch tt.tls {
+			case "1.2":
+				gcm, err = openssl.NewGCMTLS(ci)
+			case "1.3":
+				gcm, err = openssl.NewGCMTLS13(ci)
+			}
 			if err != nil {
 				t.Fatal(err)
 			}
@@ -190,9 +196,15 @@ func TestSealAndOpenTLS(t *testing.T) {
 				}
 			}
 			plainText := []byte{0x01, 0x02, 0x03}
-			additionalData := make([]byte, 13)
-			additionalData[11] = byte(len(plainText) >> 8)
-			additionalData[12] = byte(len(plainText))
+			var additionalData []byte
+			switch tt.tls {
+			case "1.2":
+				additionalData = make([]byte, 13)
+			case "1.3":
+				additionalData = []byte{23, 3, 3, 0, 0}
+			}
+			additionalData[len(additionalData)-2] = byte(len(plainText) >> 8)
+			additionalData[len(additionalData)-1] = byte(len(plainText))
 			sealed := gcm.Seal(nil, nonce[:], plainText, additionalData)
 			assertPanic(t, func() {
 				gcm.Seal(nil, nonce[:], plainText, additionalData)
diff --git a/cipher.go b/cipher.go
index 1113d067..ddaadfa8 100644
--- a/cipher.go
+++ b/cipher.go
@@ -337,7 +337,14 @@ type cipherGCM struct {
 const (
 	gcmTagSize           = 16
 	gcmStandardNonceSize = 12
-	gcmTlsAddSize        = 13
+	// TLS 1.2 additional data is constructed as:
+	//
+	//     additional_data = seq_num(8) + TLSCompressed.type(1) + TLSCompressed.version(2) + TLSCompressed.length(2);
+	gcmTls12AddSize = 13
+	// TLS 1.3 additional data is constructed as:
+	//
+	//     additional_data = TLSCiphertext.opaque_type(1) || TLSCiphertext.legacy_record_version(2) || TLSCiphertext.length(2)
+	gcmTls13AddSize      = 5
 	gcmTlsFixedNonceSize = 4
 )
 
@@ -404,8 +411,10 @@ func (g *cipherGCM) Seal(dst, nonce, plaintext, additionalData []byte) []byte {
 		panic("cipher: message too large for buffer")
 	}
 	if g.tls != cipherGCMTLSNone {
-		if len(additionalData) != gcmTlsAddSize {
-			panic("cipher: incorrect additional data length given to GCM TLS")
+		if g.tls == cipherGCMTLS12 && len(additionalData) != gcmTls12AddSize {
+			panic("cipher: incorrect additional data length given to GCM TLS 1.2")
+		} else if g.tls == cipherGCMTLS13 && len(additionalData) != gcmTls13AddSize {
+			panic("cipher: incorrect additional data length given to GCM TLS 1.3")
 		}
 		counter := binary.BigEndian.Uint64(nonce[gcmTlsFixedNonceSize:])
 		if g.tls == cipherGCMTLS13 {