diff --git a/h2quic/client.go b/h2quic/client.go
index ae1ddc45..1ec9c4be 100644
--- a/h2quic/client.go
+++ b/h2quic/client.go
@@ -241,7 +241,7 @@ func (c *client) RoundTrip(req *http.Request) (*http.Response, error) {
 	if streamEnded || isHead {
 		res.Body = noBody
 	} else {
-		res.Body = &responseBody{dataStream: dataStream}
+		res.Body = &responseBody{dataStream}
 		if requestedGzip && res.Header.Get("Content-Encoding") == "gzip" {
 			res.Header.Del("Content-Encoding")
 			res.Header.Del("Content-Length")
diff --git a/h2quic/client_test.go b/h2quic/client_test.go
index f78f799c..81006708 100644
--- a/h2quic/client_test.go
+++ b/h2quic/client_test.go
@@ -221,7 +221,7 @@ var _ = Describe("Client", func() {
 				Expect(err).ToNot(HaveOccurred())
 				Expect(rsp).To(Equal(teapot))
 				Expect(rsp.Body).To(BeAssignableToTypeOf(&responseBody{}))
-				Expect(rsp.Body.(*responseBody).dataStream).To(Equal(dataStream))
+				Expect(rsp.Body.(*responseBody).Stream).To(Equal(dataStream))
 				Expect(rsp.ContentLength).To(BeEquivalentTo(-1))
 				Expect(rsp.Request).To(Equal(request))
 				close(done)
diff --git a/h2quic/response_body.go b/h2quic/response_body.go
index f7b8d2c3..11d79e80 100644
--- a/h2quic/response_body.go
+++ b/h2quic/response_body.go
@@ -4,28 +4,15 @@ import (
 	"io"
 
 	quic "github.com/lucas-clemente/quic-go"
-	"github.com/lucas-clemente/quic-go/internal/utils"
 )
 
 type responseBody struct {
-	eofRead utils.AtomicBool
-
-	dataStream quic.Stream
+	quic.Stream
 }
 
 var _ io.ReadCloser = &responseBody{}
 
-func (rb *responseBody) Read(b []byte) (int, error) {
-	n, err := rb.dataStream.Read(b)
-	if err == io.EOF {
-		rb.eofRead.Set(true)
-	}
-	return n, err
-}
-
 func (rb *responseBody) Close() error {
-	if !rb.eofRead.Get() {
-		rb.dataStream.CancelRead(0)
-	}
+	rb.Stream.CancelRead(0)
 	return nil
 }
diff --git a/h2quic/response_body_test.go b/h2quic/response_body_test.go
index 8e1192f2..de6cf561 100644
--- a/h2quic/response_body_test.go
+++ b/h2quic/response_body_test.go
@@ -2,7 +2,6 @@ package h2quic
 
 import (
 	"bytes"
-	"io"
 
 	. "github.com/onsi/ginkgo"
 	. "github.com/onsi/gomega"
@@ -16,10 +15,10 @@ var _ = Describe("Response Body", func() {
 
 	BeforeEach(func() {
 		stream = newMockStream(42)
-		body = &responseBody{dataStream: stream}
+		body = &responseBody{stream}
 	})
 
-	It("calls CancelRead if the stream is closed before being completely read", func() {
+	It("calls CancelRead when closing", func() {
 		stream.dataToRead = *bytes.NewBuffer([]byte("foobar"))
 		n, err := body.Read(make([]byte, 3))
 		Expect(err).ToNot(HaveOccurred())
@@ -27,15 +26,4 @@ var _ = Describe("Response Body", func() {
 		Expect(body.Close()).To(Succeed())
 		Expect(stream.canceledRead).To(BeTrue())
 	})
-
-	It("doesn't calls CancelRead if the stream was completely read", func() {
-		stream.dataToRead = *bytes.NewBuffer([]byte("foobar"))
-		close(stream.unblockRead)
-		n, _ := body.Read(make([]byte, 6))
-		Expect(n).To(Equal(6))
-		_, err := body.Read(make([]byte, 6))
-		Expect(err).To(Equal(io.EOF))
-		Expect(body.Close()).To(Succeed())
-		Expect(stream.canceledRead).To(BeFalse())
-	})
 })