diff --git a/ackhandler/sent_packet_handler.go b/ackhandler/sent_packet_handler.go
index 531a99a05..686fd9d75 100644
--- a/ackhandler/sent_packet_handler.go
+++ b/ackhandler/sent_packet_handler.go
@@ -47,9 +47,7 @@ type sentPacketHandler struct {
 }
 
 // NewSentPacketHandler creates a new sentPacketHandler
-func NewSentPacketHandler() SentPacketHandler {
-	rttStats := &congestion.RTTStats{}
-
+func NewSentPacketHandler(rttStats *congestion.RTTStats) SentPacketHandler {
 	congestion := congestion.NewCubicSender(
 		congestion.DefaultClock{},
 		rttStats,
diff --git a/ackhandler/sent_packet_handler_test.go b/ackhandler/sent_packet_handler_test.go
index 59cc55141..00642b602 100644
--- a/ackhandler/sent_packet_handler_test.go
+++ b/ackhandler/sent_packet_handler_test.go
@@ -57,7 +57,8 @@ var _ = Describe("SentPacketHandler", func() {
 	)
 
 	BeforeEach(func() {
-		handler = NewSentPacketHandler().(*sentPacketHandler)
+		rttStats := &congestion.RTTStats{}
+		handler = NewSentPacketHandler(rttStats).(*sentPacketHandler)
 		streamFrame = frames.StreamFrame{
 			StreamID: 5,
 			Data:     []byte{0x13, 0x37},
diff --git a/session.go b/session.go
index 2f752999d..376538f56 100644
--- a/session.go
+++ b/session.go
@@ -9,6 +9,7 @@ import (
 	"time"
 
 	"github.com/lucas-clemente/quic-go/ackhandler"
+	"github.com/lucas-clemente/quic-go/congestion"
 	"github.com/lucas-clemente/quic-go/flowcontrol"
 	"github.com/lucas-clemente/quic-go/frames"
 	"github.com/lucas-clemente/quic-go/handshake"
@@ -51,6 +52,8 @@ type Session struct {
 
 	streamsMap *streamsMap
 
+	rttStats *congestion.RTTStats
+
 	sentPacketHandler     ackhandler.SentPacketHandler
 	receivedPacketHandler ackhandler.ReceivedPacketHandler
 	streamFramer          *streamFramer
@@ -97,7 +100,9 @@ func newSession(conn connection, v protocol.VersionNumber, connectionID protocol
 	var sentPacketHandler ackhandler.SentPacketHandler
 	var receivedPacketHandler ackhandler.ReceivedPacketHandler
 
-	sentPacketHandler = ackhandler.NewSentPacketHandler()
+	rttStats := &congestion.RTTStats{}
+
+	sentPacketHandler = ackhandler.NewSentPacketHandler(rttStats)
 	receivedPacketHandler = ackhandler.NewReceivedPacketHandler()
 
 	now := time.Now()