diff --git a/packet_unpacker.go b/packet_unpacker.go
index fc4d87eb..9b913508 100644
--- a/packet_unpacker.go
+++ b/packet_unpacker.go
@@ -31,11 +31,16 @@ func (u *packetUnpacker) Unpack(publicHeaderBinary []byte, hdr *publicHeader, r
 	}
 	r = bytes.NewReader(plaintext)
 
-	privateFlag, err := r.ReadByte()
-	if err != nil {
-		return nil, qerr.MissingPayload
+	// read private flag byte, for QUIC Version < 34
+	var entropyBit bool
+	if u.version < protocol.Version34 {
+		var privateFlag uint8
+		privateFlag, err = r.ReadByte()
+		if err != nil {
+			return nil, qerr.MissingPayload
+		}
+		entropyBit = privateFlag&0x01 > 0
 	}
-	entropyBit := privateFlag&0x01 > 0
 
 	if r.Len() == 0 {
 		return nil, qerr.MissingPayload
diff --git a/packet_unpacker_test.go b/packet_unpacker_test.go
index ee80398c..c73669cd 100644
--- a/packet_unpacker_test.go
+++ b/packet_unpacker_test.go
@@ -35,22 +35,38 @@ var _ = Describe("Packet unpacker", func() {
 	})
 
 	setReader := func(data []byte) {
-		r = bytes.NewReader(aead.Seal(0, hdrBin, append([]byte{0x01}, data...)))
+		if unpacker.version < protocol.Version34 { // add private flag
+			data = append([]byte{0x01}, data...)
+		}
+		r = bytes.NewReader(aead.Seal(0, hdrBin, data))
 	}
 
-	It("returns an error for empty packets that don't have a private flag", func() {
+	It("returns an error for empty packets that don't have a private flag, for QUIC Version < 34", func() {
 		// don't use setReader here, since it adds a private flag
+		unpacker.version = protocol.Version33
 		r = bytes.NewReader(aead.Seal(0, hdrBin, []byte{}))
 		_, err := unpacker.Unpack(hdrBin, hdr, r)
 		Expect(err).To(MatchError(qerr.MissingPayload))
 	})
 
-	It("returns an error for empty packets that have a private flag", func() {
+	It("returns an error for empty packets that have a private flag, for QUIC Version < 34", func() {
+		unpacker.version = protocol.Version33
 		setReader(nil)
 		_, err := unpacker.Unpack(hdrBin, hdr, r)
 		Expect(err).To(MatchError(qerr.MissingPayload))
 	})
 
+	It("does not read read a private flag for QUIC Version >= 34", func() {
+		unpacker.version = protocol.Version34
+		f := &frames.ConnectionCloseFrame{ReasonPhrase: "foo"}
+		err := f.Write(buf, 0)
+		Expect(err).ToNot(HaveOccurred())
+		setReader(buf.Bytes())
+		packet, err := unpacker.Unpack(hdrBin, hdr, r)
+		Expect(err).ToNot(HaveOccurred())
+		Expect(packet.frames).To(Equal([]frames.Frame{f}))
+	})
+
 	It("unpacks stream frames", func() {
 		f := &frames.StreamFrame{
 			StreamID: 1,
diff --git a/protocol/version.go b/protocol/version.go
index f13be7cf..bf646c2c 100644
--- a/protocol/version.go
+++ b/protocol/version.go
@@ -15,6 +15,7 @@ const (
 	Version31
 	Version32
 	Version33
+	Version34
 )
 
 // SupportedVersions lists the versions that the server supports