diff --git a/internal/ackhandler/packet_number_generator.go b/internal/ackhandler/packet_number_generator.go
index 4569be9a..f203892a 100644
--- a/internal/ackhandler/packet_number_generator.go
+++ b/internal/ackhandler/packet_number_generator.go
@@ -2,7 +2,8 @@ package ackhandler
 
 import (
 	"crypto/rand"
-	"math"
+	"encoding/binary"
+	mrand "math/rand"
 
 	"github.com/lucas-clemente/quic-go/internal/protocol"
 )
@@ -11,6 +12,7 @@ import (
 // it randomly skips a packet number every averagePeriod packets (on average).
 // It is guaranteed to never skip two consecutive packet numbers.
 type packetNumberGenerator struct {
+	rand          *mrand.Rand
 	averagePeriod protocol.PacketNumber
 
 	next       protocol.PacketNumber
@@ -18,7 +20,10 @@ type packetNumberGenerator struct {
 }
 
 func newPacketNumberGenerator(initial, averagePeriod protocol.PacketNumber) *packetNumberGenerator {
+	b := make([]byte, 8)
+	rand.Read(b) // it's not the end of the world if we don't get perfect random here
 	g := &packetNumberGenerator{
+		rand:          mrand.New(mrand.NewSource(int64(binary.LittleEndian.Uint64(b)))),
 		next:          initial,
 		averagePeriod: averagePeriod,
 	}
@@ -44,18 +49,6 @@ func (p *packetNumberGenerator) Pop() protocol.PacketNumber {
 }
 
 func (p *packetNumberGenerator) generateNewSkip() {
-	num := p.getRandomNumber()
-	skip := protocol.PacketNumber(num) * (p.averagePeriod - 1) / (math.MaxUint16 / 2)
 	// make sure that there are never two consecutive packet numbers that are skipped
-	p.nextToSkip = p.next + 2 + skip
-}
-
-// getRandomNumber() generates a cryptographically secure random number between 0 and MaxUint16 (= 65535)
-// The expectation value is 65535/2
-func (p *packetNumberGenerator) getRandomNumber() uint16 {
-	b := make([]byte, 2)
-	rand.Read(b) // ignore the error here
-
-	num := uint16(b[0])<<8 + uint16(b[1])
-	return num
+	p.nextToSkip = p.next + 2 + protocol.PacketNumber(p.rand.Int31n(int32(2*p.averagePeriod)))
 }
diff --git a/internal/ackhandler/packet_number_generator_test.go b/internal/ackhandler/packet_number_generator_test.go
index 73bd914f..a862a9c4 100644
--- a/internal/ackhandler/packet_number_generator_test.go
+++ b/internal/ackhandler/packet_number_generator_test.go
@@ -1,8 +1,6 @@
 package ackhandler
 
 import (
-	"math"
-
 	"github.com/lucas-clemente/quic-go/internal/protocol"
 	. "github.com/onsi/ginkgo"
 	. "github.com/onsi/gomega"
@@ -10,9 +8,10 @@ import (
 
 var _ = Describe("Packet Number Generator", func() {
 	var png *packetNumberGenerator
+	const initialPN protocol.PacketNumber = 8
 
 	BeforeEach(func() {
-		png = newPacketNumberGenerator(1, 100)
+		png = newPacketNumberGenerator(initialPN, 100)
 	})
 
 	It("can be initialized to return any first packet number", func() {
@@ -20,19 +19,18 @@ var _ = Describe("Packet Number Generator", func() {
 		Expect(png.Pop()).To(Equal(protocol.PacketNumber(12345)))
 	})
 
-	It("gets 1 as the first packet number", func() {
+	It("gets the first packet number", func() {
 		num := png.Pop()
-		Expect(num).To(Equal(protocol.PacketNumber(1)))
+		Expect(num).To(Equal(initialPN))
 	})
 
 	It("allows peeking", func() {
 		png.nextToSkip = 1000
-		Expect(png.Peek()).To(Equal(protocol.PacketNumber(1)))
-		Expect(png.Peek()).To(Equal(protocol.PacketNumber(1)))
-		num := png.Pop()
-		Expect(num).To(Equal(protocol.PacketNumber(1)))
-		Expect(png.Peek()).To(Equal(protocol.PacketNumber(2)))
-		Expect(png.Peek()).To(Equal(protocol.PacketNumber(2)))
+		Expect(png.Peek()).To(Equal(initialPN))
+		Expect(png.Peek()).To(Equal(initialPN))
+		Expect(png.Pop()).To(Equal(initialPN))
+		Expect(png.Peek()).To(Equal(initialPN + 1))
+		Expect(png.Peek()).To(Equal(initialPN + 1))
 	})
 
 	It("skips a packet number", func() {
@@ -50,51 +48,34 @@ var _ = Describe("Packet Number Generator", func() {
 	})
 
 	It("skips a specific packet number", func() {
-		png.nextToSkip = 2
-		num := png.Pop()
-		Expect(num).To(Equal(protocol.PacketNumber(1)))
-		Expect(png.Peek()).To(Equal(protocol.PacketNumber(3)))
-		num = png.Pop()
-		Expect(num).To(Equal(protocol.PacketNumber(3)))
+		png.nextToSkip = initialPN + 1
+		Expect(png.Pop()).To(Equal(initialPN))
+		Expect(png.Peek()).To(Equal(initialPN + 2))
+		Expect(png.Pop()).To(Equal(initialPN + 2))
 	})
 
 	It("generates a new packet number to skip", func() {
-		png.next = 100
-		png.averagePeriod = 100
+		const averagePeriod = 25
+		png.averagePeriod = averagePeriod
 
-		rep := 5000
-		var sum protocol.PacketNumber
-
-		for i := 0; i < rep; i++ {
-			png.generateNewSkip()
-			Expect(png.nextToSkip).ToNot(Equal(protocol.PacketNumber(101)))
-			sum += png.nextToSkip
+		periods := make([]protocol.PacketNumber, 0, 500)
+		last := initialPN
+		var lastSkip protocol.PacketNumber
+		for len(periods) < cap(periods) {
+			next := png.Pop()
+			if next > last+1 {
+				skipped := next - 1
+				Expect(skipped).To(BeNumerically(">", lastSkip+1))
+				periods = append(periods, skipped-lastSkip-1)
+				lastSkip = skipped
+			}
+			last = next
 		}
 
-		average := sum / protocol.PacketNumber(rep)
-		Expect(average).To(BeNumerically("==", protocol.PacketNumber(200), 4))
-	})
-
-	It("uses random numbers", func() {
-		var smallest uint16 = math.MaxUint16
-		var largest uint16
-		var sum uint64
-
-		rep := 10000
-
-		for i := 0; i < rep; i++ {
-			num := png.getRandomNumber()
-			sum += uint64(num)
-			if num > largest {
-				largest = num
-			}
-			if num < smallest {
-				smallest = num
-			}
+		var average float64
+		for _, p := range periods {
+			average += float64(p) / float64(len(periods))
 		}
-
-		Expect(smallest).To(BeNumerically("<", 300))
-		Expect(largest).To(BeNumerically(">", math.MaxUint16-300))
-		Expect(sum / uint64(rep)).To(BeNumerically("==", uint64(math.MaxUint16/2), 1000))
+		Expect(average).To(BeNumerically("~", averagePeriod+1 /* we never skip two packet numbers at the same time */, 5))
 	})
 })