diff --git a/http3/body.go b/http3/body.go
index e0b19321..761d0783 100644
--- a/http3/body.go
+++ b/http3/body.go
@@ -11,8 +11,6 @@ import (
 type body struct {
 	str quic.Stream
 
-	isRequest bool
-
 	// only set for the http.Response
 	// The channel is closed when the user is done with this response:
 	// either when Read() errors, or when Close() is called.
@@ -30,7 +28,6 @@ func newRequestBody(str quic.Stream, onFrameError func()) *body {
 	return &body{
 		str:          str,
 		onFrameError: onFrameError,
-		isRequest:    true,
 	}
 }
 
@@ -44,7 +41,7 @@ func newResponseBody(str quic.Stream, done chan<- struct{}, onFrameError func())
 
 func (r *body) Read(b []byte) (int, error) {
 	n, err := r.readImpl(b)
-	if err != nil && !r.isRequest {
+	if err != nil {
 		r.requestDone()
 	}
 	return n, err
@@ -86,7 +83,7 @@ func (r *body) readImpl(b []byte) (int, error) {
 }
 
 func (r *body) requestDone() {
-	if r.reqDoneClosed {
+	if r.reqDoneClosed || r.reqDone == nil {
 		return
 	}
 	close(r.reqDone)
@@ -94,11 +91,8 @@ func (r *body) requestDone() {
 }
 
 func (r *body) Close() error {
-	// quic.Stream.Close() closes the write side, not the read side
-	if r.isRequest {
-		return r.str.Close()
-	}
 	r.requestDone()
+	// If the EOF was read, CancelRead() is a no-op.
 	r.str.CancelRead(quic.ErrorCode(errorRequestCanceled))
 	return nil
 }
diff --git a/http3/body_test.go b/http3/body_test.go
index 17e90d7f..af731bd3 100644
--- a/http3/body_test.go
+++ b/http3/body_test.go
@@ -155,13 +155,6 @@ var _ = Describe("Body", func() {
 				Expect(errorCbCalled).To(BeTrue())
 			})
 
-			if bodyType == bodyTypeRequest {
-				It("closes requests", func() {
-					str.EXPECT().Close()
-					Expect(rb.Close()).To(Succeed())
-				})
-			}
-
 			if bodyType == bodyTypeResponse {
 				It("closes the reqDone channel when Read errors", func() {
 					buf.Write([]byte("invalid"))