diff --git a/quic/v3/session.go b/quic/v3/session.go
index 57641c90..fa1b1f6e 100644
--- a/quic/v3/session.go
+++ b/quic/v3/session.go
@@ -73,6 +73,9 @@ type session struct {
 	contextChan  chan context.Context
 	metrics      Metrics
 	log          *zerolog.Logger
+
+	// A special close function that we wrap with sync.Once to make sure it is only called once
+	closeFn func() error
 }
 
 func NewSession(
@@ -86,6 +89,7 @@ func NewSession(
 	log *zerolog.Logger,
 ) Session {
 	logger := log.With().Str(logFlowID, id.String()).Logger()
+	closeChan := make(chan error, 1)
 	session := &session{
 		id:             id,
 		closeAfterIdle: closeAfterIdle,
@@ -96,11 +100,19 @@ func NewSession(
 		// activeAtChan has low capacity. It can be full when there are many concurrent read/write. markActive() will
 		// drop instead of blocking because last active time only needs to be an approximation
 		activeAtChan: make(chan time.Time, 1),
-		closeChan:    make(chan error, 1),
+		closeChan:    closeChan,
 		// contextChan is an unbounded channel to help enforce one active migration of a session at a time.
 		contextChan: make(chan context.Context),
 		metrics:     metrics,
 		log:         &logger,
+		closeFn: sync.OnceValue(func() error {
+			// We don't want to block on sending to the close channel if it is already full
+			select {
+			case closeChan <- SessionCloseErr:
+			default:
+			}
+			return origin.Close()
+		}),
 	}
 	session.eyeball.Store(&eyeball)
 	return session
@@ -218,14 +230,7 @@ func (s *session) markActive() {
 
 func (s *session) Close() error {
 	// Make sure that we only close the origin connection once
-	return sync.OnceValue(func() error {
-		// We don't want to block on sending to the close channel if it is already full
-		select {
-		case s.closeChan <- SessionCloseErr:
-		default:
-		}
-		return s.origin.Close()
-	})()
+	return s.closeFn()
 }
 
 func (s *session) waitForCloseCondition(ctx context.Context, closeAfterIdle time.Duration) error {
diff --git a/quic/v3/session_test.go b/quic/v3/session_test.go
index f47ceb14..8c570074 100644
--- a/quic/v3/session_test.go
+++ b/quic/v3/session_test.go
@@ -255,11 +255,16 @@ func TestSessionClose_Multiple(t *testing.T) {
 	if !origin.closed.Load() {
 		t.Fatal("origin wasn't closed")
 	}
+	// Reset the closed status to make sure it isn't closed again
+	origin.closed.Store(false)
 	// subsequent closes shouldn't call close again or cause any errors
 	err = session.Close()
 	if err != nil {
 		t.Fatal(err)
 	}
+	if origin.closed.Load() {
+		t.Fatal("origin was incorrectly closed twice")
+	}
 }
 
 func TestSessionServe_IdleTimeout(t *testing.T) {