diff --git a/benchmarks_test.go b/benchmarks_test.go
index a4264c1..f0a85e8 100644
--- a/benchmarks_test.go
+++ b/benchmarks_test.go
@@ -90,6 +90,7 @@ func testSmallPackets(b *testing.B, n1, n2 net.Conn) {
 		wg.Add(1)
 		go func() {
 			defer wg.Done()
+			defer localB.Close()
 			receiveBuf := make([]byte, 2048)
 
 			for {
@@ -103,7 +104,7 @@ func testSmallPackets(b *testing.B, n1, n2 net.Conn) {
 				atomic.AddUint64(&receivedBytes, uint64(n))
 			}
 		}()
-
+		defer localA.Close()
 		i := 0
 		for {
 			n, err := localA.Write(msgs[i])
@@ -116,7 +117,6 @@ func testSmallPackets(b *testing.B, n1, n2 net.Conn) {
 				break
 			}
 		}
-		localA.Close()
 	})
 	b.StopTimer()
 	wg.Wait()
diff --git a/deadline.go b/deadline.go
index dd2dfaf..b251c1a 100644
--- a/deadline.go
+++ b/deadline.go
@@ -32,6 +32,11 @@ func (d *pipeDeadline) set(t time.Time) {
 	d.mu.Lock()
 	defer d.mu.Unlock()
 
+	// deadline closed
+	if d.cancel == nil {
+		return
+	}
+
 	if d.timer != nil && !d.timer.Stop() {
 		<-d.cancel // Wait for the timer callback to finish and close cancel
 	}
@@ -70,6 +75,18 @@ func (d *pipeDeadline) wait() chan struct{} {
 	return d.cancel
 }
 
+// close closes, the deadline. Any future calls to `set` will do nothing.
+func (d *pipeDeadline) close() {
+	d.mu.Lock()
+	defer d.mu.Unlock()
+
+	if d.timer != nil && !d.timer.Stop() {
+		<-d.cancel // Wait for the timer callback to finish and close cancel
+	}
+	d.timer = nil
+	d.cancel = nil
+}
+
 func isClosedChan(c <-chan struct{}) bool {
 	select {
 	case <-c:
diff --git a/go.mod b/go.mod
index f2c000f..dac7e03 100644
--- a/go.mod
+++ b/go.mod
@@ -7,6 +7,7 @@ require (
 	github.com/libp2p/go-libp2p-testing v0.1.2-0.20200422005655-8775583591d8
 	github.com/multiformats/go-varint v0.0.6
 	github.com/opentracing/opentracing-go v1.2.0 // indirect
+	go.uber.org/multierr v1.5.0
 	go.uber.org/zap v1.15.0 // indirect
 	golang.org/x/crypto v0.0.0-20190618222545-ea8f1a30c443 // indirect
 	google.golang.org/grpc v1.28.1
diff --git a/multiplex.go b/multiplex.go
index fbb80db..2ee4aad 100644
--- a/multiplex.go
+++ b/multiplex.go
@@ -111,16 +111,15 @@ func NewMultiplex(con net.Conn, initiator bool) *Multiplex {
 
 func (mp *Multiplex) newStream(id streamID, name string) (s *Stream) {
 	s = &Stream{
-		id:        id,
-		name:      name,
-		dataIn:    make(chan []byte, 8),
-		reset:     make(chan struct{}),
-		rDeadline: makePipeDeadline(),
-		wDeadline: makePipeDeadline(),
-		mp:        mp,
+		id:          id,
+		name:        name,
+		dataIn:      make(chan []byte, 8),
+		rDeadline:   makePipeDeadline(),
+		wDeadline:   makePipeDeadline(),
+		mp:          mp,
+		writeCancel: make(chan struct{}),
+		readCancel:  make(chan struct{}),
 	}
-
-	s.closedLocal, s.doCloseLocal = context.WithCancel(context.Background())
 	return
 }
 
@@ -168,7 +167,7 @@ func (mp *Multiplex) IsClosed() bool {
 	}
 }
 
-func (mp *Multiplex) sendMsg(done <-chan struct{}, header uint64, data []byte) error {
+func (mp *Multiplex) sendMsg(timeout, cancel <-chan struct{}, header uint64, data []byte) error {
 	buf := pool.Get(len(data) + 20)
 
 	n := 0
@@ -181,8 +180,10 @@ func (mp *Multiplex) sendMsg(done <-chan struct{}, header uint64, data []byte) e
 		return nil
 	case <-mp.shutdown:
 		return ErrShutdown
-	case <-done:
+	case <-timeout:
 		return errTimeout
+	case <-cancel:
+		return ErrStreamClosed
 	}
 }
 
@@ -321,7 +322,7 @@ func (mp *Multiplex) NewNamedStream(name string) (*Stream, error) {
 	ctx, cancel := context.WithTimeout(context.Background(), NewStreamTimeout)
 	defer cancel()
 
-	err := mp.sendMsg(ctx.Done(), header, []byte(name))
+	err := mp.sendMsg(ctx.Done(), nil, header, []byte(name))
 	if err != nil {
 		return nil, err
 	}
@@ -331,23 +332,20 @@ func (mp *Multiplex) NewNamedStream(name string) (*Stream, error) {
 
 func (mp *Multiplex) cleanup() {
 	mp.closeNoWait()
+
+	// Take the channels.
 	mp.chLock.Lock()
-	defer mp.chLock.Unlock()
-	for _, msch := range mp.channels {
-		msch.clLock.Lock()
-		if !msch.closedRemote {
-			msch.closedRemote = true
-			// Cancel readers
-			close(msch.reset)
-		}
+	channels := mp.channels
+	mp.channels = nil
+	mp.chLock.Unlock()
 
-		msch.doCloseLocal()
-		msch.clLock.Unlock()
+	// Cancel any reads/writes
+	for _, msch := range channels {
+		msch.cancelRead(ErrStreamReset)
+		msch.cancelWrite(ErrStreamReset)
 	}
-	// Don't remove this nil assignment. We check if this is nil to check if
-	// the connection is closed when we already have the lock (faster than
-	// checking if the stream is closed).
-	mp.channels = nil
+
+	// And... shutdown!
 	if mp.shutdownErr == nil {
 		mp.shutdownErr = ErrShutdown
 	}
@@ -421,81 +419,43 @@ func (mp *Multiplex) handleIncoming() {
 				// This is *ok*. We forget the stream on reset.
 				continue
 			}
-			msch.clLock.Lock()
-
-			isClosed := msch.isClosed()
-
-			if !msch.closedRemote {
-				close(msch.reset)
-				msch.closedRemote = true
-			}
-
-			if !isClosed {
-				msch.doCloseLocal()
-			}
 
-			msch.clLock.Unlock()
-
-			msch.cancelDeadlines()
-
-			mp.chLock.Lock()
-			delete(mp.channels, ch)
-			mp.chLock.Unlock()
+			// Cancel any ongoing reads/writes.
+			msch.cancelRead(ErrStreamReset)
+			msch.cancelWrite(ErrStreamReset)
 		case closeTag:
 			if !ok {
+				// may have canceled our reads already.
 				continue
 			}
 
-			msch.clLock.Lock()
-
-			if msch.closedRemote {
-				msch.clLock.Unlock()
-				// Technically a bug on the other side. We
-				// should consider killing the connection.
-				continue
-			}
+			// unregister and throw away future data.
+			mp.chLock.Lock()
+			delete(mp.channels, ch)
+			mp.chLock.Unlock()
 
+			// close data channel, there will be no more data.
 			close(msch.dataIn)
-			msch.closedRemote = true
-
-			cleanup := msch.isClosed()
 
-			msch.clLock.Unlock()
-
-			if cleanup {
-				msch.cancelDeadlines()
-				mp.chLock.Lock()
-				delete(mp.channels, ch)
-				mp.chLock.Unlock()
-			}
+			// We intentionally don't cancel any deadlines, cancel reads, cancel
+			// writes, etc. We just deliver the EOF by closing the
+			// data channel, and unregister the channel so we don't
+			// receive any more data. The user still needs to call
+			// `Close()` or `Reset()`.
 		case messageTag:
 			if !ok {
-				// reset stream, return b
-				pool.Put(b)
-
-				// This is a perfectly valid case when we reset
-				// and forget about the stream.
-				log.Debugf("message for non-existant stream, dropping data: %d", ch)
-				// go mp.sendResetMsg(ch.header(resetTag), false)
-				continue
-			}
-
-			msch.clLock.Lock()
-			remoteClosed := msch.closedRemote
-			msch.clLock.Unlock()
-			if remoteClosed {
-				// closed stream, return b
+				// We're not accepting data on this stream, for
+				// some reason. It's likely that we reset it, or
+				// simply canceled reads (e.g., called Close).
 				pool.Put(b)
-
-				log.Warnf("Received data from remote after stream was closed by them. (len = %d)", len(b))
-				// go mp.sendResetMsg(msch.id.header(resetTag), false)
 				continue
 			}
 
 			recvTimeout.Reset(ReceiveTimeout)
 			select {
 			case msch.dataIn <- b:
-			case <-msch.reset:
+			case <-msch.readCancel:
+				// the user has canceled reading. walk away.
 				pool.Put(b)
 			case <-recvTimeout.C:
 				pool.Put(b)
@@ -534,7 +494,7 @@ func (mp *Multiplex) sendResetMsg(header uint64, hard bool) {
 	ctx, cancel := context.WithTimeout(context.Background(), ResetStreamTimeout)
 	defer cancel()
 
-	err := mp.sendMsg(ctx.Done(), header, nil)
+	err := mp.sendMsg(ctx.Done(), nil, header, nil)
 	if err != nil && !mp.isShutdown() {
 		if hard {
 			log.Warnf("error sending reset message: %s; killing connection", err.Error())
diff --git a/multiplex_test.go b/multiplex_test.go
index 90017b2..81d484d 100644
--- a/multiplex_test.go
+++ b/multiplex_test.go
@@ -6,6 +6,8 @@ import (
 	"io/ioutil"
 	"math/rand"
 	"net"
+	"os"
+	"sync"
 	"testing"
 	"time"
 )
@@ -205,6 +207,58 @@ func TestEcho(t *testing.T) {
 	mpb.Close()
 }
 
+func TestFullClose(t *testing.T) {
+	a, b := net.Pipe()
+	mpa := NewMultiplex(a, false)
+	mpb := NewMultiplex(b, true)
+
+	mes := make([]byte, 40960)
+	acceptWait := make(chan struct{})
+	rand.Read(mes)
+	go func() {
+		s, err := mpb.Accept()
+		if err != nil {
+			t.Error(err)
+		}
+		close(acceptWait)
+
+		defer s.Close()
+
+		_, err = s.Write(mes)
+		if err != nil {
+			t.Error(err)
+		}
+	}()
+
+	s, err := mpa.NewStream()
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	<-acceptWait
+
+	err = s.Close()
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	if n, err := s.Write([]byte("foo")); err != ErrStreamClosed {
+		t.Fatal("expected stream closed error on write to closed stream, got", err)
+	} else if n != 0 {
+		t.Fatal("should not have written any bytes to closed stream")
+	}
+
+	// We closed for reading, this should fail.
+	if n, err := s.Read([]byte{0}); err != ErrStreamClosed {
+		t.Fatal("expected stream closed error on read from closed stream, got", err)
+	} else if n != 0 {
+		t.Fatal("should not have read any bytes from closed stream, got", n)
+	}
+
+	mpa.Close()
+	mpb.Close()
+}
+
 func TestHalfClose(t *testing.T) {
 	a, b := net.Pipe()
 	mpa := NewMultiplex(a, false)
@@ -216,15 +270,19 @@ func TestHalfClose(t *testing.T) {
 	go func() {
 		s, err := mpb.Accept()
 		if err != nil {
-			t.Fatal(err)
+			t.Error(err)
 		}
 
 		defer s.Close()
 
+		if err := s.CloseRead(); err != nil {
+			t.Error(err)
+		}
+
 		<-wait
 		_, err = s.Write(mes)
 		if err != nil {
-			t.Fatal(err)
+			t.Error(err)
 		}
 	}()
 
@@ -232,8 +290,9 @@ func TestHalfClose(t *testing.T) {
 	if err != nil {
 		t.Fatal(err)
 	}
+	defer s.Close()
 
-	err = s.Close()
+	err = s.CloseWrite()
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -362,6 +421,184 @@ func TestReset(t *testing.T) {
 	}
 }
 
+func TestCancelRead(t *testing.T) {
+	a, b := net.Pipe()
+
+	mpa := NewMultiplex(a, false)
+	mpb := NewMultiplex(b, true)
+
+	defer mpa.Close()
+	defer mpb.Close()
+
+	sa, err := mpa.NewStream()
+	if err != nil {
+		t.Fatal(err)
+	}
+	defer sa.Reset()
+
+	sb, err := mpb.Accept()
+	if err != nil {
+		t.Fatal(err)
+	}
+	defer sb.Reset()
+
+	// spin off a read
+	done := make(chan struct{})
+	go func() {
+		defer close(done)
+		_, err := sa.Read([]byte{0})
+		if err != ErrStreamClosed {
+			t.Error(err)
+		}
+	}()
+	// give it a chance to start.
+	time.Sleep(time.Millisecond)
+
+	// cancel it.
+	err = sa.CloseRead()
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	// It should be canceled.
+	<-done
+
+	// Writing should still succeed.
+	_, err = sa.Write([]byte("foo"))
+	if err != nil {
+		t.Fatal(err)
+	}
+	err = sa.Close()
+	if err != nil {
+		t.Fatal(err)
+	}
+	// Data should still be sent.
+	buf, err := ioutil.ReadAll(sb)
+	if err != nil {
+		t.Fatal(err)
+	}
+	if string(buf) != "foo" {
+		t.Fatalf("expected foo, got %#v", err)
+	}
+}
+
+func TestCancelWrite(t *testing.T) {
+	a, b := net.Pipe()
+
+	mpa := NewMultiplex(a, false)
+	mpb := NewMultiplex(b, true)
+
+	defer mpa.Close()
+	defer mpb.Close()
+
+	sa, err := mpa.NewStream()
+	if err != nil {
+		t.Fatal(err)
+	}
+	defer sa.Reset()
+
+	sb, err := mpb.Accept()
+	if err != nil {
+		t.Fatal(err)
+	}
+	defer sb.Reset()
+
+	// spin off a read
+	var wg sync.WaitGroup
+	wg.Add(2)
+	go func() {
+		defer wg.Done()
+		for {
+			_, err := sa.Write([]byte("foo"))
+			if err != nil {
+				if err != ErrStreamClosed {
+					t.Error("unexpected error", err)
+				}
+				return
+			}
+		}
+	}()
+	// give it a chance to fill up.
+	time.Sleep(time.Millisecond)
+
+	go func() {
+		defer wg.Done()
+		// close it.
+		err = sa.CloseWrite()
+		if err != nil {
+			t.Error(err)
+		}
+	}()
+	_, err = ioutil.ReadAll(sb)
+	if err != nil {
+		t.Fatalf("expected stream to be closed correctly")
+	}
+
+	// It should be canceled.
+	wg.Wait()
+
+	// Reading should still succeed.
+	_, err = sb.Write([]byte("bar"))
+	if err != nil {
+		t.Fatal(err)
+	}
+	err = sb.Close()
+	if err != nil {
+		t.Fatal(err)
+	}
+	// Data should still be sent.
+	buf, err := ioutil.ReadAll(sa)
+	if err != nil {
+		t.Fatal(err)
+	}
+	if string(buf) != "bar" {
+		t.Fatalf("expected foo, got %#v", err)
+	}
+}
+
+func TestCancelReadAfterWrite(t *testing.T) {
+	a, b := net.Pipe()
+
+	mpa := NewMultiplex(a, false)
+	mpb := NewMultiplex(b, true)
+
+	defer mpa.Close()
+	defer mpb.Close()
+
+	sa, err := mpa.NewStream()
+	if err != nil {
+		t.Fatal(err)
+	}
+	defer sa.Reset()
+
+	sb, err := mpb.Accept()
+	if err != nil {
+		t.Fatal(err)
+	}
+	defer sb.Reset()
+
+	// Write small messages till we would block.
+	sa.SetWriteDeadline(time.Now().Add(time.Millisecond))
+	for {
+		_, err = sa.Write([]byte("foo"))
+		if err != nil {
+			if os.IsTimeout(err) {
+				break
+			} else {
+				t.Fatal(err)
+			}
+		}
+	}
+
+	// Cancel inbound reads.
+	sb.CloseRead()
+	// We shouldn't read anything.
+	n, err := sb.Read([]byte{0})
+	if n != 0 || err != ErrStreamClosed {
+		t.Fatal("got data", err)
+	}
+}
+
 func TestResetAfterEOF(t *testing.T) {
 	a, b := net.Pipe()
 
@@ -377,7 +614,7 @@ func TestResetAfterEOF(t *testing.T) {
 	}
 	sb, err := mpb.Accept()
 
-	if err := sa.Close(); err != nil {
+	if err := sa.CloseWrite(); err != nil {
 		t.Fatal(err)
 	}
 
diff --git a/stream.go b/stream.go
index b76f75e..4d7007d 100644
--- a/stream.go
+++ b/stream.go
@@ -8,6 +8,7 @@ import (
 	"time"
 
 	pool "github.com/libp2p/go-buffer-pool"
+	"go.uber.org/multierr"
 )
 
 var (
@@ -44,15 +45,9 @@ type Stream struct {
 
 	rDeadline, wDeadline pipeDeadline
 
-	clLock       sync.Mutex
-	closedRemote bool
-
-	// Closed when the connection is reset.
-	reset chan struct{}
-
-	// Closed when the writer is closed (reset will also be closed)
-	closedLocal  context.Context
-	doCloseLocal context.CancelFunc
+	clLock                        sync.Mutex
+	writeCancelErr, readCancelErr error
+	writeCancel, readCancel       chan struct{}
 }
 
 func (s *Stream) Name() string {
@@ -74,10 +69,6 @@ func (s *Stream) preloadData() {
 
 func (s *Stream) waitForData() error {
 	select {
-	case <-s.reset:
-		// This is the only place where it's safe to return these.
-		s.returnBuffers()
-		return ErrStreamReset
 	case read, ok := <-s.dataIn:
 		if !ok {
 			return io.EOF
@@ -85,6 +76,10 @@ func (s *Stream) waitForData() error {
 		s.extra = read
 		s.exbuf = read
 		return nil
+	case <-s.readCancel:
+		// This is the only place where it's safe to return these.
+		s.returnBuffers()
+		return s.readCancelErr
 	case <-s.rDeadline.wait():
 		return errTimeout
 	}
@@ -114,10 +109,11 @@ func (s *Stream) returnBuffers() {
 
 func (s *Stream) Read(b []byte) (int, error) {
 	select {
-	case <-s.reset:
-		return 0, ErrStreamReset
+	case <-s.readCancel:
+		return 0, s.readCancelErr
 	default:
 	}
+
 	if s.extra == nil {
 		err := s.waitForData()
 		if err != nil {
@@ -162,134 +158,112 @@ func (s *Stream) Write(b []byte) (int, error) {
 }
 
 func (s *Stream) write(b []byte) (int, error) {
-	if s.isClosed() {
-		return 0, ErrStreamClosed
+	select {
+	case <-s.writeCancel:
+		return 0, s.writeCancelErr
+	default:
 	}
 
-	err := s.mp.sendMsg(s.wDeadline.wait(), s.id.header(messageTag), b)
-
+	err := s.mp.sendMsg(s.wDeadline.wait(), s.writeCancel, s.id.header(messageTag), b)
 	if err != nil {
-		if err == context.Canceled {
-			err = ErrStreamClosed
-		}
 		return 0, err
 	}
 
 	return len(b), nil
 }
 
-func (s *Stream) isClosed() bool {
-	return s.closedLocal.Err() != nil
-}
+func (s *Stream) cancelWrite(err error) bool {
+	s.wDeadline.close()
 
-func (s *Stream) Close() error {
-	ctx, cancel := context.WithTimeout(context.Background(), ResetStreamTimeout)
-	defer cancel()
+	s.clLock.Lock()
+	defer s.clLock.Unlock()
+	select {
+	case <-s.writeCancel:
+		return false
+	default:
+		s.writeCancelErr = err
+		close(s.writeCancel)
+		return true
+	}
+}
 
-	err := s.mp.sendMsg(ctx.Done(), s.id.header(closeTag), nil)
+func (s *Stream) cancelRead(err error) bool {
+	// Always unregister for reading first, even if we're already closed (or
+	// already closing). When handleIncoming calls this, it expects the
+	// stream to be unregistered by the time it returns.
+	s.mp.chLock.Lock()
+	delete(s.mp.channels, s.id)
+	s.mp.chLock.Unlock()
 
-	if s.isClosed() {
-		return nil
-	}
+	s.rDeadline.close()
 
 	s.clLock.Lock()
-	remote := s.closedRemote
-	s.clLock.Unlock()
-
-	s.doCloseLocal()
+	defer s.clLock.Unlock()
+	select {
+	case <-s.readCancel:
+		return false
+	default:
+		s.readCancelErr = err
+		close(s.readCancel)
+		return true
+	}
+}
 
-	if remote {
-		s.cancelDeadlines()
-		s.mp.chLock.Lock()
-		delete(s.mp.channels, s.id)
-		s.mp.chLock.Unlock()
+func (s *Stream) CloseWrite() error {
+	if !s.cancelWrite(ErrStreamClosed) {
+		// Check if we closed the stream _nicely_. If so, we don't need
+		// to report an error to the user.
+		if s.writeCancelErr == ErrStreamClosed {
+			return nil
+		}
+		// Closed for some other reason. Report it.
+		return s.writeCancelErr
 	}
 
+	ctx, cancel := context.WithTimeout(context.Background(), ResetStreamTimeout)
+	defer cancel()
+
+	err := s.mp.sendMsg(ctx.Done(), nil, s.id.header(closeTag), nil)
+	// We failed to close the stream after 2 minutes, something is probably wrong.
 	if err != nil && !s.mp.isShutdown() {
 		log.Warnf("Error closing stream: %s; killing connection", err.Error())
 		s.mp.Close()
 	}
-
 	return err
 }
 
-func (s *Stream) Reset() error {
-	s.clLock.Lock()
-
-	// Don't reset when fully closed.
-	if s.closedRemote && s.isClosed() {
-		s.clLock.Unlock()
-		return nil
-	}
-
-	// Don't reset twice.
-	select {
-	case <-s.reset:
-		s.clLock.Unlock()
-		return nil
-	default:
-	}
-
-	close(s.reset)
-	s.doCloseLocal()
-	s.closedRemote = true
-	s.cancelDeadlines()
-
-	go s.mp.sendResetMsg(s.id.header(resetTag), true)
-
-	s.clLock.Unlock()
-
-	s.mp.chLock.Lock()
-	delete(s.mp.channels, s.id)
-	s.mp.chLock.Unlock()
-
+func (s *Stream) CloseRead() error {
+	s.cancelRead(ErrStreamClosed)
 	return nil
 }
 
-func (s *Stream) cancelDeadlines() {
-	s.rDeadline.set(time.Time{})
-	s.wDeadline.set(time.Time{})
+func (s *Stream) Close() error {
+	return multierr.Combine(s.CloseRead(), s.CloseWrite())
 }
 
-func (s *Stream) SetDeadline(t time.Time) error {
-	s.clLock.Lock()
-	defer s.clLock.Unlock()
-
-	if s.closedRemote && s.isClosed() {
-		return errStreamClosed
-	}
+func (s *Stream) Reset() error {
+	s.cancelRead(ErrStreamReset)
 
-	if !s.closedRemote {
-		s.rDeadline.set(t)
+	if s.cancelWrite(ErrStreamReset) {
+		// Send a reset in the background.
+		go s.mp.sendResetMsg(s.id.header(resetTag), true)
 	}
 
-	if !s.isClosed() {
-		s.wDeadline.set(t)
-	}
+	return nil
+}
 
+func (s *Stream) SetDeadline(t time.Time) error {
+	s.rDeadline.set(t)
+	s.wDeadline.set(t)
 	return nil
 }
 
 func (s *Stream) SetReadDeadline(t time.Time) error {
-	s.clLock.Lock()
-	defer s.clLock.Unlock()
-
-	if s.closedRemote {
-		return errStreamClosed
-	}
-
 	s.rDeadline.set(t)
 	return nil
 }
 
 func (s *Stream) SetWriteDeadline(t time.Time) error {
-	s.clLock.Lock()
-	defer s.clLock.Unlock()
-
-	if s.isClosed() {
-		return errStreamClosed
-	}
-
 	s.wDeadline.set(t)
 	return nil
 }