diff --git a/Changelog.md b/Changelog.md
index 941a6d6d..7a5a8e5d 100644
--- a/Changelog.md
+++ b/Changelog.md
@@ -2,7 +2,7 @@
 
 ## v0.6.0 (unreleased)
 
-- Add support for QUIC 38 and 39, drop support for QUIC 35
+- Add support for QUIC 38 and 39, drop support for QUIC 35 and 36
 - Added `quic.Config` options for maximal flow control windows
 - Add a `quic.Config` option for QUIC versions
 - Add a `quic.Config` option to request truncation of the connection ID from a server
diff --git a/client_test.go b/client_test.go
index 3b5dd13f..78043b7f 100644
--- a/client_test.go
+++ b/client_test.go
@@ -508,7 +508,7 @@ var _ = Describe("Client", func() {
 				ConnectionID:    0x1337,
 			}
 			b := &bytes.Buffer{}
-			err := ph.Write(b, protocol.Version36, protocol.PerspectiveServer)
+			err := ph.Write(b, cl.version, protocol.PerspectiveServer)
 			Expect(err).ToNot(HaveOccurred())
 			packetConn.dataToRead = b.Bytes()
 
diff --git a/internal/crypto/null_aead.go b/internal/crypto/null_aead.go
index e1cc6135..fa1ccb7b 100644
--- a/internal/crypto/null_aead.go
+++ b/internal/crypto/null_aead.go
@@ -7,8 +7,5 @@ func NewNullAEAD(p protocol.Perspective, v protocol.VersionNumber) AEAD {
 	if v.UsesTLS() {
 		return &nullAEADFNV64a{}
 	}
-	return &nullAEADFNV128a{
-		perspective: p,
-		version:     v,
-	}
+	return &nullAEADFNV128a{perspective: p}
 }
diff --git a/internal/crypto/null_aead_fnv128a.go b/internal/crypto/null_aead_fnv128a.go
index 5e49aa98..ecc4010b 100644
--- a/internal/crypto/null_aead_fnv128a.go
+++ b/internal/crypto/null_aead_fnv128a.go
@@ -11,7 +11,6 @@ import (
 // nullAEAD handles not-yet encrypted packets
 type nullAEADFNV128a struct {
 	perspective protocol.Perspective
-	version     protocol.VersionNumber
 }
 
 var _ AEAD = &nullAEADFNV128a{}
@@ -25,12 +24,10 @@ func (n *nullAEADFNV128a) Open(dst, src []byte, packetNumber protocol.PacketNumb
 	hash := fnv128a.New()
 	hash.Write(associatedData)
 	hash.Write(src[12:])
-	if n.version >= protocol.Version37 {
-		if n.perspective == protocol.PerspectiveServer {
-			hash.Write([]byte("Client"))
-		} else {
-			hash.Write([]byte("Server"))
-		}
+	if n.perspective == protocol.PerspectiveServer {
+		hash.Write([]byte("Client"))
+	} else {
+		hash.Write([]byte("Server"))
 	}
 	testHigh, testLow := hash.Sum128()
 
@@ -55,12 +52,10 @@ func (n *nullAEADFNV128a) Seal(dst, src []byte, packetNumber protocol.PacketNumb
 	hash.Write(associatedData)
 	hash.Write(src)
 
-	if n.version >= protocol.Version37 {
-		if n.perspective == protocol.PerspectiveServer {
-			hash.Write([]byte("Server"))
-		} else {
-			hash.Write([]byte("Client"))
-		}
+	if n.perspective == protocol.PerspectiveServer {
+		hash.Write([]byte("Server"))
+	} else {
+		hash.Write([]byte("Client"))
 	}
 
 	high, low := hash.Sum128()
diff --git a/internal/crypto/null_aead_fnv128a_test.go b/internal/crypto/null_aead_fnv128a_test.go
index e632986c..9fbc2a77 100644
--- a/internal/crypto/null_aead_fnv128a_test.go
+++ b/internal/crypto/null_aead_fnv128a_test.go
@@ -11,32 +11,37 @@ var _ = Describe("NullAEAD using FNV128a", func() {
 	plainText := []byte("They are endowed with reason and conscience and should act towards one another in a spirit of brotherhood.")
 	hash36 := []byte{0x98, 0x9b, 0x33, 0x3f, 0xe8, 0xde, 0x32, 0x5c, 0xa6, 0x7f, 0x9c, 0xf7}
 
-	It("opens", func() {
-		cipherText := append(hash36, plainText...)
-		aead := NewNullAEAD(protocol.PerspectiveServer, protocol.Version36)
-		res, err := aead.Open(nil, cipherText, 0, aad)
-		Expect(err).ToNot(HaveOccurred())
-		Expect(res).To(Equal(plainText))
+	var aeadServer AEAD
+	var aeadClient AEAD
+
+	BeforeEach(func() {
+		aeadServer = NewNullAEAD(protocol.PerspectiveServer, protocol.Version37)
+		aeadClient = NewNullAEAD(protocol.PerspectiveClient, protocol.Version37)
 	})
 
-	It("seals", func() {
-		aead := NewNullAEAD(protocol.PerspectiveServer, protocol.Version36)
-		sealed := aead.Seal(nil, plainText, 0, aad)
-		Expect(sealed).To(Equal(append(hash36, plainText...)))
-		Expect(sealed).To(HaveLen(len(plainText) + aead.Overhead()))
+	It("seals and opens, client => server", func() {
+		cipherText := aeadClient.Seal(nil, plainText, 0, aad)
+		res, err := aeadServer.Open(nil, cipherText, 0, aad)
+		Expect(err).ToNot(HaveOccurred())
+		Expect(res).To(Equal([]byte("They are endowed with reason and conscience and should act towards one another in a spirit of brotherhood.")))
+	})
+
+	It("seals and opens, server => client", func() {
+		cipherText := aeadServer.Seal(nil, plainText, 0, aad)
+		res, err := aeadClient.Open(nil, cipherText, 0, aad)
+		Expect(err).ToNot(HaveOccurred())
+		Expect(res).To(Equal([]byte("They are endowed with reason and conscience and should act towards one another in a spirit of brotherhood.")))
 	})
 
 	It("rejects short ciphertexts", func() {
-		aead := NewNullAEAD(protocol.PerspectiveServer, protocol.Version36)
-		_, err := aead.Open(nil, nil, 0, nil)
+		_, err := aeadServer.Open(nil, nil, 0, nil)
 		Expect(err).To(MatchError("NullAEAD: ciphertext cannot be less than 12 bytes long"))
 	})
 
 	It("seals in-place", func() {
-		aead := NewNullAEAD(protocol.PerspectiveServer, protocol.Version36)
 		buf := make([]byte, 6, 12+6)
 		copy(buf, []byte("foobar"))
-		res := aead.Seal(buf[0:0], buf, 0, nil)
+		res := aeadServer.Seal(buf[0:0], buf, 0, nil)
 		buf = buf[:12+6]
 		Expect(buf[12:]).To(Equal([]byte("foobar")))
 		Expect(res[12:]).To(Equal([]byte("foobar")))
@@ -44,32 +49,7 @@ var _ = Describe("NullAEAD using FNV128a", func() {
 
 	It("fails", func() {
 		cipherText := append(append(hash36, plainText...), byte(0x42))
-		aead := NewNullAEAD(protocol.PerspectiveServer, protocol.Version36)
-		_, err := aead.Open(nil, cipherText, 0, aad)
+		_, err := aeadClient.Open(nil, cipherText, 0, aad)
 		Expect(err).To(HaveOccurred())
 	})
-
-	Context("including the perspective, for QUIC >= 37", func() {
-		var aeadServer AEAD
-		var aeadClient AEAD
-
-		BeforeEach(func() {
-			aeadServer = NewNullAEAD(protocol.PerspectiveServer, protocol.Version37)
-			aeadClient = NewNullAEAD(protocol.PerspectiveClient, protocol.Version37)
-		})
-
-		It("opens, for QUIC version >= 37, as a server", func() {
-			cipherText := aeadClient.Seal(nil, plainText, 0, aad)
-			res, err := aeadServer.Open(nil, cipherText, 0, aad)
-			Expect(err).ToNot(HaveOccurred())
-			Expect(res).To(Equal([]byte("They are endowed with reason and conscience and should act towards one another in a spirit of brotherhood.")))
-		})
-
-		It("opens, for QUIC version >= 37, as a client", func() {
-			cipherText := aeadServer.Seal(nil, plainText, 0, aad)
-			res, err := aeadClient.Open(nil, cipherText, 0, aad)
-			Expect(err).ToNot(HaveOccurred())
-			Expect(res).To(Equal([]byte("They are endowed with reason and conscience and should act towards one another in a spirit of brotherhood.")))
-		})
-	})
 })
diff --git a/internal/crypto/null_aead_test.go b/internal/crypto/null_aead_test.go
index a456f541..092dd9b9 100644
--- a/internal/crypto/null_aead_test.go
+++ b/internal/crypto/null_aead_test.go
@@ -10,7 +10,6 @@ var _ = Describe("NullAEAD", func() {
 	It("selects the right FVN variant", func() {
 		Expect(NewNullAEAD(protocol.PerspectiveClient, protocol.Version39)).To(Equal(&nullAEADFNV128a{
 			perspective: protocol.PerspectiveClient,
-			version:     protocol.Version39,
 		}))
 		Expect(NewNullAEAD(protocol.PerspectiveClient, protocol.VersionTLS)).To(Equal(&nullAEADFNV64a{}))
 	})
diff --git a/internal/handshake/connection_parameters_manager_test.go b/internal/handshake/connection_parameters_manager_test.go
index b1ff4d1d..e5d02972 100644
--- a/internal/handshake/connection_parameters_manager_test.go
+++ b/internal/handshake/connection_parameters_manager_test.go
@@ -22,14 +22,14 @@ var _ = Describe("ConnectionsParameterManager", func() {
 	BeforeEach(func() {
 		cpm = NewConnectionParamatersManager(
 			protocol.PerspectiveServer,
-			protocol.Version36,
+			protocol.VersionWhatever,
 			maxReceiveStreamFlowControlWindowServer,
 			maxReceiveConnectionFlowControlWindowServer,
 			idleTimeout,
 		).(*connectionParametersManager)
 		cpmClient = NewConnectionParamatersManager(
 			protocol.PerspectiveClient,
-			protocol.Version36,
+			protocol.VersionWhatever,
 			maxReceiveStreamFlowControlWindowClient,
 			maxReceiveConnectionFlowControlWindowClient,
 			idleTimeout,
diff --git a/internal/handshake/crypto_setup_client_test.go b/internal/handshake/crypto_setup_client_test.go
index 9e3a2e31..181427bc 100644
--- a/internal/handshake/crypto_setup_client_test.go
+++ b/internal/handshake/crypto_setup_client_test.go
@@ -107,7 +107,7 @@ var _ = Describe("Client Crypto Setup", func() {
 
 		stream = newMockStream()
 		certManager = &mockCertManager{}
-		version := protocol.Version36
+		version := protocol.Version37
 		aeadChanged = make(chan protocol.EncryptionLevel, 2)
 		csInt, err := NewCryptoSetupClient(
 			"hostname",
@@ -216,10 +216,11 @@ var _ = Describe("Client Crypto Setup", func() {
 			})
 
 			It("doesn't care about unsupported versions", func() {
-				cs.negotiatedVersions = []protocol.VersionNumber{protocol.VersionUnsupported, protocol.Version36, protocol.VersionUnsupported}
+				ver := protocol.SupportedVersions[0]
+				cs.negotiatedVersions = []protocol.VersionNumber{protocol.VersionUnsupported, ver, protocol.VersionUnsupported}
 				b := &bytes.Buffer{}
 				b.Write([]byte{0, 0, 0, 0})
-				utils.LittleEndian.WriteUint32(b, protocol.VersionNumberToTag(protocol.Version36))
+				utils.LittleEndian.WriteUint32(b, protocol.VersionNumberToTag(ver))
 				b.Write([]byte{0x13, 0x37, 0x13, 0x37})
 				Expect(cs.validateVersionList(b.Bytes())).To(BeTrue())
 			})
@@ -411,10 +412,11 @@ var _ = Describe("Client Crypto Setup", func() {
 		})
 
 		It("accepts a SHLO after a version negotiation", func() {
-			cs.negotiatedVersions = []protocol.VersionNumber{protocol.Version36}
+			ver := protocol.SupportedVersions[0]
+			cs.negotiatedVersions = []protocol.VersionNumber{ver}
 			cs.receivedSecurePacket = true
 			b := &bytes.Buffer{}
-			utils.LittleEndian.WriteUint32(b, protocol.VersionNumberToTag(protocol.Version36))
+			utils.LittleEndian.WriteUint32(b, protocol.VersionNumberToTag(ver))
 			shloMap[TagVER] = b.Bytes()
 			err := cs.handleSHLOMessage(shloMap)
 			Expect(err).ToNot(HaveOccurred())
@@ -486,7 +488,7 @@ var _ = Describe("Client Crypto Setup", func() {
 			Expect(err).ToNot(HaveOccurred())
 			Expect(string(tags[TagSNI])).To(Equal(cs.hostname))
 			Expect(tags[TagPDMD]).To(Equal([]byte("X509")))
-			Expect(tags[TagVER]).To(Equal([]byte("Q036")))
+			Expect(tags[TagVER]).To(Equal([]byte("Q037")))
 			Expect(tags[TagCCS]).To(Equal(certManager.commonCertificateHashes))
 			Expect(tags).ToNot(HaveKey(TagTCID))
 		})
diff --git a/internal/protocol/version.go b/internal/protocol/version.go
index 12cf91d8..5f269808 100644
--- a/internal/protocol/version.go
+++ b/internal/protocol/version.go
@@ -5,8 +5,7 @@ type VersionNumber int
 
 // The version numbers, making grepping easier
 const (
-	Version36 VersionNumber = 36 + iota
-	Version37
+	Version37 VersionNumber = 37 + iota
 	Version38
 	Version39
 	VersionTLS         VersionNumber = 101
@@ -21,7 +20,6 @@ var SupportedVersions = []VersionNumber{
 	Version39,
 	Version38,
 	Version37,
-	Version36,
 }
 
 // UsesTLS says if this QUIC version uses TLS 1.3 for the handshake
diff --git a/internal/protocol/version_test.go b/internal/protocol/version_test.go
index fbaa2410..4f7436c7 100644
--- a/internal/protocol/version_test.go
+++ b/internal/protocol/version_test.go
@@ -7,7 +7,6 @@ import (
 
 var _ = Describe("Version", func() {
 	It("says if a version supports TLS", func() {
-		Expect(Version36.UsesTLS()).To(BeFalse())
 		Expect(Version37.UsesTLS()).To(BeFalse())
 		Expect(Version38.UsesTLS()).To(BeFalse())
 		Expect(Version39.UsesTLS()).To(BeFalse())
diff --git a/internal/utils/byteorder_test.go b/internal/utils/byteorder_test.go
index 16ba55c2..7547bafe 100644
--- a/internal/utils/byteorder_test.go
+++ b/internal/utils/byteorder_test.go
@@ -8,8 +8,8 @@ import (
 
 var _ = Describe("Byte Order", func() {
 	It("says little Little Endian before QUIC 39", func() {
-		Expect(GetByteOrder(protocol.Version36)).To(Equal(LittleEndian))
 		Expect(GetByteOrder(protocol.Version37)).To(Equal(LittleEndian))
+		Expect(GetByteOrder(protocol.Version38)).To(Equal(LittleEndian))
 	})
 
 	It("says little Little Endian for QUIC 39", func() {
diff --git a/internal/wire/public_header_test.go b/internal/wire/public_header_test.go
index 5c42f33d..4ff9d6cf 100644
--- a/internal/wire/public_header_test.go
+++ b/internal/wire/public_header_test.go
@@ -365,7 +365,7 @@ var _ = Describe("Public Header", func() {
 				b := &bytes.Buffer{}
 				hdr := PublicHeader{
 					VersionFlag:     true,
-					VersionNumber:   protocol.Version36,
+					VersionNumber:   protocol.Version38,
 					ConnectionID:    0x4cfa9f9b668619f6,
 					PacketNumber:    0x1337,
 					PacketNumberLen: protocol.PacketNumberLen6,
@@ -377,7 +377,7 @@ var _ = Describe("Public Header", func() {
 				firstByte, _ := b.ReadByte()
 				Expect(firstByte & 0x01).To(Equal(uint8(1)))
 				Expect(firstByte & 0x30).To(Equal(uint8(0x30)))
-				Expect(string(b.Bytes()[8:12])).To(Equal("Q036"))
+				Expect(string(b.Bytes()[8:12])).To(Equal("Q038"))
 				Expect(b.Bytes()[12:18]).To(Equal([]byte{0x37, 0x13, 0, 0, 0, 0}))
 			})
 		})
@@ -455,7 +455,7 @@ var _ = Describe("Public Header", func() {
 					PacketNumber:         0xDECAFBAD,
 					PacketNumberLen:      protocol.PacketNumberLen6,
 					VersionFlag:          true,
-					VersionNumber:        protocol.Version36,
+					VersionNumber:        versionLittleEndian,
 				}
 				length, err := hdr.GetLength(protocol.PerspectiveClient)
 				Expect(err).ToNot(HaveOccurred())
diff --git a/packet_unpacker_test.go b/packet_unpacker_test.go
index f51bae2c..238e0a3f 100644
--- a/packet_unpacker_test.go
+++ b/packet_unpacker_test.go
@@ -17,7 +17,7 @@ type mockAEAD struct {
 }
 
 func (m *mockAEAD) Open(dst, src []byte, packetNumber protocol.PacketNumber, associatedData []byte) ([]byte, protocol.EncryptionLevel, error) {
-	nullAEAD := crypto.NewNullAEAD(protocol.PerspectiveServer, protocol.VersionWhatever)
+	nullAEAD := crypto.NewNullAEAD(protocol.PerspectiveClient, protocol.VersionWhatever)
 	res, err := nullAEAD.Open(dst, src, packetNumber, associatedData)
 	return res, m.encLevelOpen, err
 }