diff --git a/internal/protocol/version.go b/internal/protocol/version.go
index f9bfef363..bf206c017 100644
--- a/internal/protocol/version.go
+++ b/internal/protocol/version.go
@@ -68,6 +68,17 @@ func (vn VersionNumber) CryptoStreamID() StreamID {
 	return 0
 }
 
+// StreamContributesToConnectionFlowControl says if a stream contributes to connection-level flow control
+func (vn VersionNumber) StreamContributesToConnectionFlowControl(id StreamID) bool {
+	if id == vn.CryptoStreamID() {
+		return false
+	}
+	if vn.isGQUIC() && id == 3 {
+		return false
+	}
+	return true
+}
+
 func (vn VersionNumber) isGQUIC() bool {
 	return vn > gquicVersion0 && vn <= maxGquicVersion
 }
diff --git a/internal/protocol/version_test.go b/internal/protocol/version_test.go
index 5a23aea4a..6d9fff3e3 100644
--- a/internal/protocol/version_test.go
+++ b/internal/protocol/version_test.go
@@ -52,6 +52,21 @@ var _ = Describe("Version", func() {
 		Expect(VersionTLS.CryptoStreamID()).To(Equal(StreamID(0)))
 	})
 
+	It("says if a stream contributes to connection-level flowcontrol, for gQUIC", func() {
+		Expect(Version39.StreamContributesToConnectionFlowControl(1)).To(BeFalse())
+		Expect(Version39.StreamContributesToConnectionFlowControl(2)).To(BeTrue())
+		Expect(Version39.StreamContributesToConnectionFlowControl(3)).To(BeFalse())
+		Expect(Version39.StreamContributesToConnectionFlowControl(4)).To(BeTrue())
+		Expect(Version39.StreamContributesToConnectionFlowControl(5)).To(BeTrue())
+	})
+
+	It("says if a stream contributes to connection-level flowcontrol, for TLS", func() {
+		Expect(VersionTLS.StreamContributesToConnectionFlowControl(0)).To(BeFalse())
+		Expect(VersionTLS.StreamContributesToConnectionFlowControl(1)).To(BeTrue())
+		Expect(VersionTLS.StreamContributesToConnectionFlowControl(2)).To(BeTrue())
+		Expect(VersionTLS.StreamContributesToConnectionFlowControl(3)).To(BeTrue())
+	})
+
 	It("recognizes supported versions", func() {
 		Expect(IsSupportedVersion(SupportedVersions, 0)).To(BeFalse())
 		Expect(IsSupportedVersion(SupportedVersions, SupportedVersions[0])).To(BeTrue())
diff --git a/session.go b/session.go
index b92110120..34c820a32 100644
--- a/session.go
+++ b/session.go
@@ -818,18 +818,13 @@ func (s *session) queueResetStreamFrame(id protocol.StreamID, offset protocol.By
 }
 
 func (s *session) newStream(id protocol.StreamID) streamI {
-	// TODO: find a better solution for determining which streams contribute to connection level flow control
-	var contributesToConnection bool
-	if id != 0 && id != 1 && id != 3 {
-		contributesToConnection = true
-	}
 	var initialSendWindow protocol.ByteCount
 	if s.peerParams != nil {
 		initialSendWindow = s.peerParams.StreamFlowControlWindow
 	}
 	flowController := flowcontrol.NewStreamFlowController(
 		id,
-		contributesToConnection,
+		s.version.StreamContributesToConnectionFlowControl(id),
 		s.connFlowController,
 		protocol.ReceiveStreamFlowControlWindow,
 		protocol.ByteCount(s.config.MaxReceiveStreamFlowControlWindow),