diff --git a/h2quic/response_writer_test.go b/h2quic/response_writer_test.go
index 16b0d817..0a042585 100644
--- a/h2quic/response_writer_test.go
+++ b/h2quic/response_writer_test.go
@@ -12,11 +12,12 @@ import (
 type mockStream struct {
 	id protocol.StreamID
 	bytes.Buffer
+	remoteClosed bool
 }
 
-func (mockStream) Close() error                          { return nil }
-func (mockStream) CloseRemote(offset protocol.ByteCount) { panic("not implemented") }
-func (s mockStream) StreamID() protocol.StreamID         { return s.id }
+func (mockStream) Close() error                             { return nil }
+func (s *mockStream) CloseRemote(offset protocol.ByteCount) { s.remoteClosed = true }
+func (s mockStream) StreamID() protocol.StreamID            { return s.id }
 
 var _ = Describe("Response Writer", func() {
 	var (
diff --git a/h2quic/server.go b/h2quic/server.go
index eb416bd8..23ead498 100644
--- a/h2quic/server.go
+++ b/h2quic/server.go
@@ -99,6 +99,10 @@ func (s *Server) handleRequest(session streamCreator, headerStream utils.Stream,
 		return err
 	}
 
+	if h2headersFrame.StreamEnded() {
+		dataStream.CloseRemote(0)
+	}
+
 	// stream's Close() closes the write side, not the read side
 	req.Body = ioutil.NopCloser(dataStream)
 
diff --git a/h2quic/server_test.go b/h2quic/server_test.go
index 1d71f159..85c3499b 100644
--- a/h2quic/server_test.go
+++ b/h2quic/server_test.go
@@ -15,19 +15,21 @@ import (
 )
 
 type mockSession struct {
-	closed bool
+	closed     bool
+	dataStream *mockStream
 }
 
 func (s *mockSession) GetOrOpenStream(id protocol.StreamID) (utils.Stream, error) {
-	return &mockStream{}, nil
+	return s.dataStream, nil
 }
 
 func (s *mockSession) Close(error) error { s.closed = true; return nil }
 
 var _ = Describe("H2 server", func() {
 	var (
-		s       *Server
-		session *mockSession
+		s          *Server
+		session    *mockSession
+		dataStream *mockStream
 	)
 
 	BeforeEach(func() {
@@ -35,7 +37,8 @@ var _ = Describe("H2 server", func() {
 		s, err = NewServer(testdata.GetTLSConfig())
 		Expect(err).NotTo(HaveOccurred())
 		Expect(s).NotTo(BeNil())
-		session = &mockSession{}
+		dataStream = &mockStream{}
+		session = &mockSession{dataStream: dataStream}
 	})
 
 	It("uses default handler", func() {
@@ -66,7 +69,24 @@ var _ = Describe("H2 server", func() {
 			h2framer = http2.NewFramer(nil, headerStream)
 		})
 
-		It("handles a sample request", func() {
+		It("handles a sample GET request", func() {
+			var handlerCalled bool
+			s.handler = http.HandlerFunc(func(w http.ResponseWriter, r *http.Request) {
+				Expect(r.Host).To(Equal("www.example.com"))
+				handlerCalled = true
+			})
+			headerStream.Write([]byte{
+				0x0, 0x0, 0x11, 0x1, 0x5, 0x0, 0x0, 0x0, 0x5,
+				// Taken from https://http2.github.io/http2-spec/compression.html#request.examples.with.huffman.coding
+				0x82, 0x86, 0x84, 0x41, 0x8c, 0xf1, 0xe3, 0xc2, 0xe5, 0xf2, 0x3a, 0x6b, 0xa0, 0xab, 0x90, 0xf4, 0xff,
+			})
+			err := s.handleRequest(session, headerStream, hpackDecoder, h2framer)
+			Expect(err).NotTo(HaveOccurred())
+			Eventually(func() bool { return handlerCalled }).Should(BeTrue())
+			Expect(dataStream.remoteClosed).To(BeTrue())
+		})
+
+		It("does not close the dataStream when end of stream is not set", func() {
 			var handlerCalled bool
 			s.handler = http.HandlerFunc(func(w http.ResponseWriter, r *http.Request) {
 				Expect(r.Host).To(Equal("www.example.com"))
@@ -80,6 +100,7 @@ var _ = Describe("H2 server", func() {
 			err := s.handleRequest(session, headerStream, hpackDecoder, h2framer)
 			Expect(err).NotTo(HaveOccurred())
 			Eventually(func() bool { return handlerCalled }).Should(BeTrue())
+			Expect(dataStream.remoteClosed).To(BeFalse())
 		})
 	})