diff --git a/buffer.go b/buffer.go
index 50e206a..cb979a3 100644
--- a/buffer.go
+++ b/buffer.go
@@ -7,19 +7,27 @@ type buffer struct {
 	data []byte
 }
 
-func (b *buffer) Read(p []byte) (n int, err error) {
-	n = len(b.data) - b.read
-	if n == 0 {
-		return 0, io.EOF
-	}
-
-	if len(p) < n {
-		n = len(p)
-	}
-
-	copy(p[:n], b.data[b.read:b.read+n])
+// From the io.Reader documentation:
+//
+// When Read encounters an error or end-of-file condition after
+// successfully reading n > 0 bytes, it returns the number of
+// bytes read.  It may return the (non-nil) error from the same call
+// or return the error (and n == 0) from a subsequent call.
+// An instance of this general case is that a Reader returning
+// a non-zero number of bytes at the end of the input stream may
+// return either err == EOF or err == nil.  The next Read should
+// return 0, EOF.
+//
+// This function implements the latter behaviour, returning the
+// (non-nil) error from the same call.
+func (b *buffer) Read(p []byte) (int, error) {
+	var err error
+	n := copy(p, b.data[b.read:])
 	b.read += n
-	return
+	if b.read == len(b.data) {
+		err = io.EOF
+	}
+	return n, err
 }
 
 func (b *buffer) Len() int {
diff --git a/buffer_test.go b/buffer_test.go
index 8a7a564..ba1f00d 100644
--- a/buffer_test.go
+++ b/buffer_test.go
@@ -9,10 +9,12 @@ import (
 func TestBuffer(t *testing.T) {
 	writeBytes := []byte("deadbeef")
 
+	const numWrites = 10
+
 	var b buffer
-	for i := 0; i < 10; i++ {
+	for i := 0; i < numWrites; i++ {
 		n, err := b.Write(writeBytes)
-		if err != nil {
+		if err != nil && err != io.EOF {
 			t.Fatal(err)
 		}
 		if n != len(writeBytes) {
@@ -22,9 +24,14 @@ func TestBuffer(t *testing.T) {
 
 	for j := 0; j < 2; j++ {
 		readBytes := make([]byte, len(writeBytes))
-		for i := 0; i < 10; i++ {
+		for i := 0; i < numWrites; i++ {
 			n, err := b.Read(readBytes)
-			if err != nil {
+			if i == numWrites-1 {
+				// The last read should report EOF.
+				if err != io.EOF {
+					t.Fatal(err)
+				}
+			} else if err != nil {
 				t.Fatal(err)
 			}
 			if n != len(readBytes) {
@@ -34,10 +41,13 @@ func TestBuffer(t *testing.T) {
 				t.Errorf("different bytes read: want=%d got=%d", writeBytes, readBytes)
 			}
 		}
-		_, err := b.Read(readBytes)
+		n, err := b.Read(readBytes)
 		if err != io.EOF {
 			t.Errorf("expected EOF")
 		}
+		if n != 0 {
+			t.Errorf("expected buffer to be empty, but got %d bytes", n)
+		}
 
 		b.resetRead()
 	}
@@ -55,18 +65,26 @@ func TestBufferOffset(t *testing.T) {
 		t.Fatalf("cannot write all the bytes: want=%d got=%d", len(writeBytes), n)
 	}
 
-	for i := 0; i < len(writeBytes)/2; i++ {
-		readBytes := make([]byte, 2)
+	const readSize = 2
+
+	numReads := len(writeBytes) / readSize
+
+	for i := 0; i < numReads; i++ {
+		readBytes := make([]byte, readSize)
 		n, err := b.Read(readBytes)
-		if err != nil {
+		if i == numReads-1 {
+			// The last read should report EOF.
+			if err != io.EOF {
+				t.Fatal(err)
+			}
+		} else if err != nil {
 			t.Fatal(err)
 		}
-		if n != 2 {
-			t.Fatalf("cannot read the bytes: want=%d got=%d", 2, n)
+		if n != readSize {
+			t.Fatalf("cannot read the bytes: want=%d got=%d", readSize, n)
 		}
-		if !bytes.Equal(readBytes, writeBytes[i*2:i*2+2]) {
-			t.Fatalf("different bytes read: want=%s got=%s",
-				readBytes, writeBytes[i*2:i*2+2])
+		if got := writeBytes[i*readSize : i*readSize+readSize]; !bytes.Equal(got, readBytes) {
+			t.Fatalf("different bytes read: want=%s got=%s", readBytes, got)
 		}
 	}
 }
diff --git a/cmux.go b/cmux.go
index e124799..10a8932 100644
--- a/cmux.go
+++ b/cmux.go
@@ -186,13 +186,26 @@ func newMuxConn(c net.Conn) *MuxConn {
 	}
 }
 
-func (m *MuxConn) Read(b []byte) (n int, err error) {
-	if n, err = m.buf.Read(b); err == nil {
-		return
+// From the io.Reader documentation:
+//
+// When Read encounters an error or end-of-file condition after
+// successfully reading n > 0 bytes, it returns the number of
+// bytes read.  It may return the (non-nil) error from the same call
+// or return the error (and n == 0) from a subsequent call.
+// An instance of this general case is that a Reader returning
+// a non-zero number of bytes at the end of the input stream may
+// return either err == EOF or err == nil.  The next Read should
+// return 0, EOF.
+//
+// This function implements the latter behaviour, returning the
+// (non-nil) error from the same call.
+func (m *MuxConn) Read(b []byte) (int, error) {
+	n1, err := m.buf.Read(b)
+	if n1 == len(b) || err != io.EOF {
+		return n1, err
 	}
-
-	n, err = m.Conn.Read(b)
-	return
+	n2, err := m.Conn.Read(b[n1:])
+	return n1 + n2, err
 }
 
 func (m *MuxConn) sniffer() io.Reader {
diff --git a/cmux_test.go b/cmux_test.go
index 433763c..531aae3 100644
--- a/cmux_test.go
+++ b/cmux_test.go
@@ -3,6 +3,7 @@ package cmux
 import (
 	"errors"
 	"fmt"
+	"io"
 	"io/ioutil"
 	"net"
 	"net/http"
@@ -164,6 +165,48 @@ func runTestRPCClient(t *testing.T, addr net.Addr) {
 	}
 }
 
+func TestRead(t *testing.T) {
+	defer leakCheck(t)()
+	errCh := make(chan error)
+	defer func() {
+		select {
+		case err := <-errCh:
+			t.Fatal(err)
+		default:
+		}
+	}()
+	const payload = "hello world\r\n"
+	const mult = 2
+
+	writer, reader := net.Pipe()
+	go func() {
+		if _, err := io.WriteString(writer, strings.Repeat(payload, mult)); err != nil {
+			t.Fatal(err)
+		}
+	}()
+
+	l := newChanListener()
+	defer close(l.connCh)
+	l.connCh <- reader
+	muxl := New(l)
+	// Register a bogus matcher to force reading from the conn.
+	muxl.Match(HTTP2())
+	anyl := muxl.Match(Any())
+	go safeServe(errCh, muxl)
+	muxedConn, err := anyl.Accept()
+	if err != nil {
+		t.Fatal(err)
+	}
+	var b [mult * len(payload)]byte
+	n, err := muxedConn.Read(b[:])
+	if err != nil {
+		t.Fatal(err)
+	}
+	if e := len(b); n != e {
+		t.Errorf("expected to read %d bytes, but read %d bytes", e, n)
+	}
+}
+
 func TestAny(t *testing.T) {
 	defer leakCheck(t)()
 	errCh := make(chan error)