diff --git a/fuzzing/internal/helper/export.go b/fuzzing/internal/helper/helper.go
similarity index 83%
rename from fuzzing/internal/helper/export.go
rename to fuzzing/internal/helper/helper.go
index db55fb9d..1513c3fa 100644
--- a/fuzzing/internal/helper/export.go
+++ b/fuzzing/internal/helper/helper.go
@@ -8,6 +8,14 @@ import (
 	"path/filepath"
 )
 
+// NthBit gets the n-th bit of a byte (counting starts at 0).
+func NthBit(val uint8, n int) bool {
+	if n < 0 || n > 7 {
+		panic("invalid value for n")
+	}
+	return val>>n&0x1 == 1
+}
+
 // WriteCorpusFile writes data to a corpus file in directory path.
 // The filename is calculated from the SHA1 sum of the file contents.
 func WriteCorpusFile(path string, data []byte) error {
diff --git a/fuzzing/internal/helper/export_test.go b/fuzzing/internal/helper/helper_test.go
similarity index 82%
rename from fuzzing/internal/helper/export_test.go
rename to fuzzing/internal/helper/helper_test.go
index 3f6adc48..6bee7d91 100644
--- a/fuzzing/internal/helper/export_test.go
+++ b/fuzzing/internal/helper/helper_test.go
@@ -57,4 +57,16 @@ var _ = Describe("exporting", func() {
 		Expect(WriteCorpusFile(subdir, []byte("lorem ipsum"))).To(Succeed())
 		Expect(subdir).To(BeADirectory())
 	})
+
+	It("gets the nth bit of a byte", func() {
+		const val = 0b10010001
+		Expect(NthBit(val, 0)).To(BeTrue())
+		Expect(NthBit(val, 1)).To(BeFalse())
+		Expect(NthBit(val, 2)).To(BeFalse())
+		Expect(NthBit(val, 3)).To(BeFalse())
+		Expect(NthBit(val, 4)).To(BeTrue())
+		Expect(NthBit(val, 5)).To(BeFalse())
+		Expect(NthBit(val, 6)).To(BeFalse())
+		Expect(NthBit(val, 7)).To(BeTrue())
+	})
 })
diff --git a/fuzzing/transportparameters/cmd/corpus.go b/fuzzing/transportparameters/cmd/corpus.go
index c9105aef..8c88a6a8 100644
--- a/fuzzing/transportparameters/cmd/corpus.go
+++ b/fuzzing/transportparameters/cmd/corpus.go
@@ -1,14 +1,15 @@
 package main
 
 import (
-	"fmt"
+	"bytes"
 	"log"
 	"math"
 	"math/rand"
 	"net"
-	"os"
 	"time"
 
+	"github.com/lucas-clemente/quic-go/fuzzing/internal/helper"
+	"github.com/lucas-clemente/quic-go/fuzzing/transportparameters"
 	"github.com/lucas-clemente/quic-go/internal/protocol"
 
 	"github.com/lucas-clemente/quic-go/internal/wire"
@@ -26,8 +27,7 @@ func getRandomValue() uint64 {
 }
 
 func main() {
-	rand.Seed(1337)
-	for i := 0; i < 20; i++ {
+	for i := 0; i < 30; i++ {
 		tp := &wire.TransportParameters{
 			InitialMaxStreamDataBidiLocal:  protocol.ByteCount(getRandomValue()),
 			InitialMaxStreamDataBidiRemote: protocol.ByteCount(getRandomValue()),
@@ -69,24 +69,21 @@ func main() {
 				StatelessResetToken: token,
 			}
 		}
-		pers := protocol.PerspectiveServer
+
+		var data []byte
 		if rand.Int()%2 == 0 {
-			pers = protocol.PerspectiveClient
+			pers := protocol.PerspectiveServer
+			if rand.Int()%2 == 0 {
+				pers = protocol.PerspectiveClient
+			}
+			data = tp.Marshal(pers)
+		} else {
+			b := &bytes.Buffer{}
+			tp.MarshalForSessionTicket(b)
+			data = b.Bytes()
 		}
-		if err := writeCorpusFile(fmt.Sprintf("tp%d", i), tp.Marshal(pers)); err != nil {
+		if err := helper.WriteCorpusFileWithPrefix("corpus", data, transportparameters.PrefixLen); err != nil {
 			log.Fatal(err)
 		}
 	}
 }
-
-func writeCorpusFile(name string, data []byte) error {
-	file, err := os.Create("corpus/" + name)
-	if err != nil {
-		return err
-	}
-	data = append(getRandomData(2), data...)
-	if _, err := file.Write(data); err != nil {
-		return err
-	}
-	return file.Close()
-}
diff --git a/fuzzing/transportparameters/corpus/tp0 b/fuzzing/transportparameters/corpus/tp0
deleted file mode 100644
index d3c24448..00000000
Binary files a/fuzzing/transportparameters/corpus/tp0 and /dev/null differ
diff --git a/fuzzing/transportparameters/corpus/tp1 b/fuzzing/transportparameters/corpus/tp1
deleted file mode 100644
index be6b122f..00000000
Binary files a/fuzzing/transportparameters/corpus/tp1 and /dev/null differ
diff --git a/fuzzing/transportparameters/corpus/tp10 b/fuzzing/transportparameters/corpus/tp10
deleted file mode 100644
index 9a8d202b..00000000
Binary files a/fuzzing/transportparameters/corpus/tp10 and /dev/null differ
diff --git a/fuzzing/transportparameters/corpus/tp11 b/fuzzing/transportparameters/corpus/tp11
deleted file mode 100644
index 561deb59..00000000
Binary files a/fuzzing/transportparameters/corpus/tp11 and /dev/null differ
diff --git a/fuzzing/transportparameters/corpus/tp12 b/fuzzing/transportparameters/corpus/tp12
deleted file mode 100644
index 3d4ccd4d..00000000
Binary files a/fuzzing/transportparameters/corpus/tp12 and /dev/null differ
diff --git a/fuzzing/transportparameters/corpus/tp13 b/fuzzing/transportparameters/corpus/tp13
deleted file mode 100644
index c43110c3..00000000
Binary files a/fuzzing/transportparameters/corpus/tp13 and /dev/null differ
diff --git a/fuzzing/transportparameters/corpus/tp14 b/fuzzing/transportparameters/corpus/tp14
deleted file mode 100644
index a9693444..00000000
Binary files a/fuzzing/transportparameters/corpus/tp14 and /dev/null differ
diff --git a/fuzzing/transportparameters/corpus/tp15 b/fuzzing/transportparameters/corpus/tp15
deleted file mode 100644
index e4da18fc..00000000
Binary files a/fuzzing/transportparameters/corpus/tp15 and /dev/null differ
diff --git a/fuzzing/transportparameters/corpus/tp16 b/fuzzing/transportparameters/corpus/tp16
deleted file mode 100644
index 164fa983..00000000
Binary files a/fuzzing/transportparameters/corpus/tp16 and /dev/null differ
diff --git a/fuzzing/transportparameters/corpus/tp17 b/fuzzing/transportparameters/corpus/tp17
deleted file mode 100644
index 8a9a1164..00000000
Binary files a/fuzzing/transportparameters/corpus/tp17 and /dev/null differ
diff --git a/fuzzing/transportparameters/corpus/tp18 b/fuzzing/transportparameters/corpus/tp18
deleted file mode 100644
index ec202f0a..00000000
Binary files a/fuzzing/transportparameters/corpus/tp18 and /dev/null differ
diff --git a/fuzzing/transportparameters/corpus/tp19 b/fuzzing/transportparameters/corpus/tp19
deleted file mode 100644
index 6557eac3..00000000
Binary files a/fuzzing/transportparameters/corpus/tp19 and /dev/null differ
diff --git a/fuzzing/transportparameters/corpus/tp2 b/fuzzing/transportparameters/corpus/tp2
deleted file mode 100644
index 0966dc25..00000000
Binary files a/fuzzing/transportparameters/corpus/tp2 and /dev/null differ
diff --git a/fuzzing/transportparameters/corpus/tp3 b/fuzzing/transportparameters/corpus/tp3
deleted file mode 100644
index d93ffcef..00000000
Binary files a/fuzzing/transportparameters/corpus/tp3 and /dev/null differ
diff --git a/fuzzing/transportparameters/corpus/tp4 b/fuzzing/transportparameters/corpus/tp4
deleted file mode 100644
index 6802692a..00000000
Binary files a/fuzzing/transportparameters/corpus/tp4 and /dev/null differ
diff --git a/fuzzing/transportparameters/corpus/tp5 b/fuzzing/transportparameters/corpus/tp5
deleted file mode 100644
index 1091419e..00000000
Binary files a/fuzzing/transportparameters/corpus/tp5 and /dev/null differ
diff --git a/fuzzing/transportparameters/corpus/tp6 b/fuzzing/transportparameters/corpus/tp6
deleted file mode 100644
index 1b087fb9..00000000
Binary files a/fuzzing/transportparameters/corpus/tp6 and /dev/null differ
diff --git a/fuzzing/transportparameters/corpus/tp7 b/fuzzing/transportparameters/corpus/tp7
deleted file mode 100644
index 5e1e148e..00000000
Binary files a/fuzzing/transportparameters/corpus/tp7 and /dev/null differ
diff --git a/fuzzing/transportparameters/corpus/tp8 b/fuzzing/transportparameters/corpus/tp8
deleted file mode 100644
index 209384b5..00000000
Binary files a/fuzzing/transportparameters/corpus/tp8 and /dev/null differ
diff --git a/fuzzing/transportparameters/corpus/tp9 b/fuzzing/transportparameters/corpus/tp9
deleted file mode 100644
index 8775295d..00000000
Binary files a/fuzzing/transportparameters/corpus/tp9 and /dev/null differ
diff --git a/fuzzing/transportparameters/fuzz.go b/fuzzing/transportparameters/fuzz.go
index 18b20eea..0b352953 100644
--- a/fuzzing/transportparameters/fuzz.go
+++ b/fuzzing/transportparameters/fuzz.go
@@ -4,28 +4,32 @@ import (
 	"bytes"
 	"fmt"
 
+	"github.com/lucas-clemente/quic-go/fuzzing/internal/helper"
 	"github.com/lucas-clemente/quic-go/internal/protocol"
 	"github.com/lucas-clemente/quic-go/internal/wire"
 )
 
+// PrefixLen is the number of bytes used for configuration
+const PrefixLen = 1
+
+// Fuzz fuzzes the QUIC transport parameters.
 //go:generate go run ./cmd/corpus.go
 func Fuzz(data []byte) int {
-	if len(data) <= 1 {
+	if len(data) <= PrefixLen {
 		return 0
 	}
 
-	if data[0]%2 == 0 {
-		return fuzzTransportParametersForSessionTicket(data[1:])
+	if helper.NthBit(data[0], 0) {
+		return fuzzTransportParametersForSessionTicket(data[PrefixLen:])
 	}
-	return fuzzTransportParameters(data[1:])
+	return fuzzTransportParameters(data[PrefixLen:], helper.NthBit(data[0], 1))
 }
 
-func fuzzTransportParameters(data []byte) int {
-	perspective := protocol.PerspectiveServer
-	if data[0]%2 == 1 {
+func fuzzTransportParameters(data []byte, isServer bool) int {
+	perspective := protocol.PerspectiveClient
+	if isServer {
 		perspective = protocol.PerspectiveServer
 	}
-	data = data[1:]
 
 	tp := &wire.TransportParameters{}
 	if err := tp.Unmarshal(data, perspective); err != nil {