diff --git a/internal/handshake/transport_parameter_test.go b/internal/handshake/transport_parameter_test.go
index 1628c4ac1..48ccc3711 100644
--- a/internal/handshake/transport_parameter_test.go
+++ b/internal/handshake/transport_parameter_test.go
@@ -139,10 +139,16 @@ var _ = Describe("Transport Parameters", func() {
 	})
 
 	It("doesn't send the max_ack_delay, if it has the default value", func() {
-		dataDefault := (&TransportParameters{MaxAckDelay: protocol.DefaultMaxAckDelay}).Marshal()
-		defaultLen := len(dataDefault)
-		data := (&TransportParameters{MaxAckDelay: protocol.DefaultMaxAckDelay + time.Millisecond}).Marshal()
-		Expect(len(data)).To(Equal(defaultLen + 2 /* parameter ID */ + 2 /* length field */ + 1 /* value */))
+		const num = 1000
+		var defaultLen, dataLen int
+		// marshal 1000 times to average out the greasing transport parameter
+		for i := 0; i < num; i++ {
+			dataDefault := (&TransportParameters{MaxAckDelay: protocol.DefaultMaxAckDelay}).Marshal()
+			defaultLen += len(dataDefault)
+			data := (&TransportParameters{MaxAckDelay: protocol.DefaultMaxAckDelay + time.Millisecond}).Marshal()
+			dataLen += len(data)
+		}
+		Expect(float32(dataLen) / num).To(BeNumerically("~", float32(defaultLen)/num+2 /* parameter ID */ +2 /* length field */ +1 /* value */, 1))
 	})
 
 	It("errors when the ack_delay_exponenent is too large", func() {
@@ -152,10 +158,16 @@ var _ = Describe("Transport Parameters", func() {
 	})
 
 	It("doesn't send the ack_delay_exponent, if it has the default value", func() {
-		dataDefault := (&TransportParameters{AckDelayExponent: protocol.DefaultAckDelayExponent}).Marshal()
-		defaultLen := len(dataDefault)
-		data := (&TransportParameters{AckDelayExponent: protocol.DefaultAckDelayExponent + 1}).Marshal()
-		Expect(len(data)).To(Equal(defaultLen + 2 /* parameter ID */ + 2 /* length field */ + 1 /* value */))
+		const num = 1000
+		var defaultLen, dataLen int
+		// marshal 1000 times to average out the greasing transport parameter
+		for i := 0; i < num; i++ {
+			dataDefault := (&TransportParameters{AckDelayExponent: protocol.DefaultAckDelayExponent}).Marshal()
+			defaultLen += len(dataDefault)
+			data := (&TransportParameters{AckDelayExponent: protocol.DefaultAckDelayExponent + 1}).Marshal()
+			dataLen += len(data)
+		}
+		Expect(float32(dataLen) / num).To(BeNumerically("~", float32(defaultLen)/num+2 /* parameter ID */ +2 /* length field */ +1 /* value */, 1))
 	})
 
 	It("sets the default value for the ack_delay_exponent, when no value was sent", func() {
diff --git a/internal/handshake/transport_parameters.go b/internal/handshake/transport_parameters.go
index 724c3586e..0c9928046 100644
--- a/internal/handshake/transport_parameters.go
+++ b/internal/handshake/transport_parameters.go
@@ -6,6 +6,7 @@ import (
 	"errors"
 	"fmt"
 	"io"
+	"math/rand"
 	"sort"
 	"time"
 
@@ -13,6 +14,10 @@ import (
 	"github.com/lucas-clemente/quic-go/internal/utils"
 )
 
+func init() {
+	rand.Seed(time.Now().UTC().UnixNano())
+}
+
 type transportParameterID uint16
 
 const (
@@ -204,6 +209,14 @@ func (p *TransportParameters) Marshal() []byte {
 	b := &bytes.Buffer{}
 	b.Write([]byte{0, 0}) // length. Will be replaced later
 
+	// add a greased value
+	utils.BigEndian.WriteUint16(b, uint16(27+31*rand.Intn(100)))
+	len := rand.Intn(16)
+	randomData := make([]byte, len)
+	rand.Read(randomData)
+	utils.BigEndian.WriteUint16(b, uint16(len))
+	b.Write(randomData)
+
 	// initial_max_stream_data_bidi_local
 	p.marshalVarintParam(b, initialMaxStreamDataBidiLocalParameterID, uint64(p.InitialMaxStreamDataBidiLocal))
 	// initial_max_stream_data_bidi_remote