diff --git a/internal/congestion/bandwidth.go b/internal/congestion/bandwidth.go
index 54269c56..96b1c5aa 100644
--- a/internal/congestion/bandwidth.go
+++ b/internal/congestion/bandwidth.go
@@ -1,6 +1,7 @@
 package congestion
 
 import (
+	"math"
 	"time"
 
 	"github.com/lucas-clemente/quic-go/internal/protocol"
@@ -9,6 +10,8 @@ import (
 // Bandwidth of a connection
 type Bandwidth uint64
 
+const infBandwidth Bandwidth = math.MaxUint64
+
 const (
 	// BitsPerSecond is 1 bit per second
 	BitsPerSecond Bandwidth = 1
diff --git a/internal/congestion/cubic_sender.go b/internal/congestion/cubic_sender.go
index ef0d7650..1d9d540c 100644
--- a/internal/congestion/cubic_sender.go
+++ b/internal/congestion/cubic_sender.go
@@ -276,7 +276,7 @@ func (c *cubicSender) BandwidthEstimate() Bandwidth {
 	srtt := c.rttStats.SmoothedRTT()
 	if srtt == 0 {
 		// If we haven't measured an rtt, the bandwidth estimate is unknown.
-		return 0
+		return infBandwidth
 	}
 	return BandwidthFromDelta(c.GetCongestionWindow(), srtt)
 }
diff --git a/internal/congestion/cubic_sender_test.go b/internal/congestion/cubic_sender_test.go
index 21d189cc..90f8789c 100644
--- a/internal/congestion/cubic_sender_test.go
+++ b/internal/congestion/cubic_sender_test.go
@@ -98,6 +98,7 @@ var _ = Describe("Cubic Sender", func() {
 	})
 
 	It("paces", func() {
+		rttStats.UpdateRTT(10*time.Millisecond, 0, time.Now())
 		clock.Advance(time.Hour)
 		// Fill the send window with data, then verify that we can't send.
 		SendAvailableSendWindow()
@@ -129,7 +130,7 @@ var _ = Describe("Cubic Sender", func() {
 		// At startup make sure we can send.
 		Expect(sender.CanSend(0)).To(BeTrue())
 		Expect(sender.TimeUntilSend(0)).To(BeZero())
-		Expect(sender.BandwidthEstimate()).To(BeZero())
+		Expect(sender.BandwidthEstimate()).To(Equal(infBandwidth))
 		// Make sure we can send.
 		Expect(sender.TimeUntilSend(0)).To(BeZero())