diff --git a/conn.go b/conn.go
index cf32fa4..e3aa63b 100644
--- a/conn.go
+++ b/conn.go
@@ -1,7 +1,12 @@
 package libp2ptls
 
 import (
+	"bytes"
 	"crypto/tls"
+	"errors"
+	"fmt"
+	"io"
+	"net"
 
 	ci "github.com/libp2p/go-libp2p-core/crypto"
 	"github.com/libp2p/go-libp2p-core/peer"
@@ -35,3 +40,117 @@ func (c *conn) RemotePeer() peer.ID {
 func (c *conn) RemotePublicKey() ci.PubKey {
 	return c.remotePubKey
 }
+
+const (
+	recordTypeHandshake byte = 22
+	versionTLS13             = 0x0304
+	maxCiphertextTLS13       = 16384 + 256 // maximum ciphertext length in TLS 1.3
+	maxHandshake             = 65536       // maximum handshake we support (protocol max is 16 MB)
+)
+
+var errSimultaneousConnect = errors.New("detected TCP simultaneous connect")
+
+type teeConn struct {
+	net.Conn
+	buf *bytes.Buffer
+}
+
+func newTeeConn(c net.Conn, buf *bytes.Buffer) net.Conn {
+	return &teeConn{Conn: c, buf: buf}
+}
+
+func (c *teeConn) Read(b []byte) (int, error) {
+	n, err := c.Conn.Read(b)
+	c.buf.Write(b[:n])
+	return n, err
+}
+
+type wrappedConn struct {
+	// Before reading the first handshake message, this is a *teeConn.
+	// After reading the first handshake message, we switch it to the rawConn.
+	net.Conn
+
+	rawConn             net.Conn
+	hasReadFirstMessage bool
+	raw                 *bytes.Buffer // contains a copy of every byte of the first handshake message we read from the wire
+
+	hand bytes.Buffer // used to store the first handshake message until we've completely read it
+}
+
+func newWrappedConn(c net.Conn) net.Conn {
+	wc := &wrappedConn{
+		raw:     &bytes.Buffer{},
+		rawConn: c,
+	}
+	wc.Conn = newTeeConn(c, wc.raw)
+	return wc
+}
+
+func (c *wrappedConn) Read(b []byte) (int, error) {
+	if c.hasReadFirstMessage {
+		return c.Conn.Read(b)
+	}
+
+	// We read the first handshake message, and it was not a ClientHello.
+	// We now need to feed all the bytes we read from the wire into the TLS stack,
+	// so it can proceed with the handshake.
+	if c.raw.Len() > 0 {
+		n, err := c.raw.Read(b)
+		if err == io.EOF || c.raw.Len() == 0 {
+			c.raw = nil
+			c.Conn = c.rawConn
+			c.hasReadFirstMessage = true
+			err = nil
+		}
+		return n, err
+	}
+
+	mes, err := c.readFirstHandshakeMessage()
+	if err != nil {
+		return 0, err
+	}
+
+	switch mes[0] {
+	case 1: // ClientHello
+		return 0, errSimultaneousConnect
+	case 2: // ServerHello
+		return c.Read(b)
+	default:
+		return 0, fmt.Errorf("unexpected message type: %d", mes[0])
+	}
+}
+
+func (c *wrappedConn) readFirstHandshakeMessage() ([]byte, error) {
+	for c.hand.Len() < 4 {
+		if err := c.readRecord(); err != nil {
+			return nil, err
+		}
+	}
+	data := c.hand.Bytes()
+	n := int(data[1])<<16 | int(data[2])<<8 | int(data[3])
+	if n > maxHandshake {
+		return nil, fmt.Errorf("tls: handshake message of length %d bytes exceeds maximum of %d bytes", n, maxHandshake)
+	}
+	for c.hand.Len() < 4+n {
+		if err := c.readRecord(); err != nil {
+			return nil, err
+		}
+	}
+	return c.hand.Next(4 + n), nil
+}
+
+func (c *wrappedConn) readRecord() error {
+	hdr := make([]byte, 5)
+	if _, err := io.ReadFull(c.Conn, hdr); err != nil {
+		return err
+	}
+	if hdr[0] != recordTypeHandshake {
+		return errors.New("expected a handshake record")
+	}
+	n := int(hdr[3])<<8 | int(hdr[4])
+	if n > maxCiphertextTLS13 {
+		return fmt.Errorf("oversized record received with length %d", n)
+	}
+	_, err := io.CopyN(&c.hand, c.Conn, int64(n))
+	return err
+}
diff --git a/crypto.go b/crypto.go
index 14e1db0..40358a5 100644
--- a/crypto.go
+++ b/crypto.go
@@ -1,9 +1,11 @@
 package libp2ptls
 
 import (
+	"bytes"
 	"crypto/ecdsa"
 	"crypto/elliptic"
 	"crypto/rand"
+	"crypto/sha256"
 	"crypto/tls"
 	"crypto/x509"
 	"crypto/x509/pkix"
@@ -220,3 +222,11 @@ func preferServerCipherSuites() bool {
 	)
 	return !hasGCMAsm
 }
+
+// Compare two peer IDs by their SHA256 hash.
+// The result will be 0 if H(a) == H(b), -1 if H(a) < H(b), and +1 if H(a) > H(b).
+func comparePeerIDs(p1, p2 peer.ID) int {
+	p1Hash := sha256.Sum256([]byte(p1))
+	p2Hash := sha256.Sum256([]byte(p2))
+	return bytes.Compare(p1Hash[:], p2Hash[:])
+}
diff --git a/transport.go b/transport.go
index 214853c..9f53de9 100644
--- a/transport.go
+++ b/transport.go
@@ -70,11 +70,28 @@ func (t *Transport) SecureInbound(ctx context.Context, insecure net.Conn) (sec.S
 // notice this after 1 RTT when calling Read.
 func (t *Transport) SecureOutbound(ctx context.Context, insecure net.Conn, p peer.ID) (sec.SecureConn, error) {
 	config, keyCh := t.identity.ConfigForPeer(p)
-	cs, err := t.handshake(ctx, tls.Client(insecure, config), keyCh)
-	if err != nil {
+	conn, err := t.handshake(ctx, tls.Client(newWrappedConn(insecure), config), keyCh)
+	if err == errSimultaneousConnect {
+		switch comparePeerIDs(t.localPeer, p) {
+		case 0:
+			return nil, errors.New("tried to simultaneous connect to oneself")
+		case -1:
+			// SHA256(our peer ID) is smaller than SHA256(their peer ID).
+			// We're the client in the next connection attempt.
+			config, keyCh := t.identity.ConfigForPeer(p)
+			return t.handshake(ctx, tls.Client(insecure, config), keyCh)
+		case 1:
+			// SHA256(our peer ID) is larger than SHA256(their peer ID).
+			// We're the server in the next connection attempt.
+			config, keyCh := t.identity.ConfigForPeer(p)
+			return t.handshake(ctx, tls.Server(insecure, config), keyCh)
+		default:
+			panic("unexpected peer ID comparison result")
+		}
+	} else if err != nil {
 		insecure.Close()
 	}
-	return cs, err
+	return conn, err
 }
 
 func (t *Transport) handshake(
diff --git a/transport_test.go b/transport_test.go
index 94f2c21..ab52d21 100644
--- a/transport_test.go
+++ b/transport_test.go
@@ -15,6 +15,7 @@ import (
 	"math/big"
 	mrand "math/rand"
 	"net"
+	"reflect"
 	"time"
 
 	"github.com/onsi/gomega/gbytes"
@@ -188,6 +189,62 @@ var _ = Describe("Transport", func() {
 		Eventually(done).Should(BeClosed())
 	})
 
+	It("handles simultaneous open", func() {
+		// Avoid confusion regarding the naming.
+		p1, p1Key := serverID, serverKey
+		p2, p2Key := clientID, clientKey
+
+		// We use a normal dial / listen to establish the TCP connection,
+		// but we then start two clients.
+		c1raw, c2raw := connect()
+
+		c1Transport, err := New(p1Key)
+		Expect(err).ToNot(HaveOccurred())
+		c2Transport, err := New(p2Key)
+		Expect(err).ToNot(HaveOccurred())
+
+		c1ConnChan := make(chan sec.SecureConn, 1)
+		go func() {
+			defer GinkgoRecover()
+			conn, err := c1Transport.SecureOutbound(context.Background(), c1raw, p2)
+			Expect(err).ToNot(HaveOccurred())
+			c1ConnChan <- conn
+		}()
+
+		c2, err := c2Transport.SecureOutbound(context.Background(), c2raw, p1)
+		Expect(err).ToNot(HaveOccurred())
+		defer c2.Close()
+		var c1 sec.SecureConn
+		Eventually(c1ConnChan).Should(Receive(&c1))
+		defer c1.Close()
+
+		// check that the peers are in the correct roles
+		isClient := func(c sec.SecureConn) bool {
+			// the isClient field of the tls.Conn will tell us who is client and server
+			return reflect.ValueOf(c.(*conn).Conn).Elem().FieldByName("isClient").Bool()
+		}
+		switch comparePeerIDs(p1, p2) {
+		case -1:
+			// H(p1) < H(p2) => p1 acts as a client, p2 as a server
+			Expect(isClient(c1)).To(BeTrue())
+			Expect(isClient(c2)).To(BeFalse())
+		case 1:
+			// H(p1) > H(p2) => p1 acts as a server, p2 as a client
+			Expect(isClient(c1)).To(BeFalse())
+			Expect(isClient(c2)).To(BeTrue())
+		default:
+			Fail("unexpected peer comparison result")
+		}
+
+		// exchange some data
+		_, err = c1.Write([]byte("foobar"))
+		Expect(err).ToNot(HaveOccurred())
+		b := make([]byte, 6)
+		_, err = c2.Read(b)
+		Expect(err).ToNot(HaveOccurred())
+		Expect(string(b)).To(Equal("foobar"))
+	})
+
 	Context("invalid certificates", func() {
 		invalidateCertChain := func(identity *Identity) {
 			switch identity.config.Certificates[0].PrivateKey.(type) {