diff --git a/integrationtests/gquic/drop_test.go b/integrationtests/gquic/drop_test.go
index 2d471261..cffa3fb4 100644
--- a/integrationtests/gquic/drop_test.go
+++ b/integrationtests/gquic/drop_test.go
@@ -3,6 +3,7 @@ package gquic_test
 import (
 	"bytes"
 	"fmt"
+	mrand "math/rand"
 	"os/exec"
 	"strconv"
 
@@ -13,20 +14,25 @@ import (
 
 	. "github.com/onsi/ginkgo"
 	. "github.com/onsi/gomega"
+	. "github.com/onsi/gomega/gbytes"
 	. "github.com/onsi/gomega/gexec"
 )
 
+var directions = []quicproxy.Direction{quicproxy.DirectionIncoming, quicproxy.DirectionOutgoing, quicproxy.DirectionBoth}
+
 var _ = Describe("Drop tests", func() {
 	var proxy *quicproxy.QuicProxy
 
-	runDropTest := func(dropCallback quicproxy.DropCallback, version protocol.VersionNumber) {
+	startProxy := func(dropCallback quicproxy.DropCallback, version protocol.VersionNumber) {
 		var err error
 		proxy, err = quicproxy.NewQuicProxy("localhost:0", version, &quicproxy.Opts{
 			RemoteAddr: "localhost:" + testserver.Port(),
 			DropPacket: dropCallback,
 		})
 		Expect(err).ToNot(HaveOccurred())
+	}
 
+	downloadFile := func(version protocol.VersionNumber) {
 		command := exec.Command(
 			clientPath,
 			"--quic-version="+strconv.Itoa(int(version)),
@@ -34,7 +40,6 @@ var _ = Describe("Drop tests", func() {
 			"--port="+strconv.Itoa(proxy.LocalPort()),
 			"https://quic.clemente.io/prdata",
 		)
-
 		session, err := Start(command, nil, GinkgoWriter)
 		Expect(err).NotTo(HaveOccurred())
 		defer session.Kill()
@@ -42,46 +47,91 @@ var _ = Describe("Drop tests", func() {
 		Expect(bytes.Contains(session.Out.Contents(), testserver.PRData)).To(BeTrue())
 	}
 
+	downloadHello := func(version protocol.VersionNumber) {
+		command := exec.Command(
+			clientPath,
+			"--quic-version="+strconv.Itoa(int(version)),
+			"--host=127.0.0.1",
+			"--port="+strconv.Itoa(proxy.LocalPort()),
+			"https://quic.clemente.io/hello",
+		)
+		session, err := Start(command, nil, GinkgoWriter)
+		Expect(err).NotTo(HaveOccurred())
+		defer session.Kill()
+		Eventually(session, 20).Should(Exit(0))
+		Expect(session.Out).To(Say(":status 200"))
+		Expect(session.Out).To(Say("body: Hello, World!\n"))
+	}
+
+	deterministicDropper := func(p, interval, dropInARow uint64) bool {
+		return (p % interval) < dropInARow
+	}
+
+	stochasticDropper := func(freq int) bool {
+		return mrand.Int63n(int64(freq)) == 0
+	}
+
 	AfterEach(func() {
 		Expect(proxy.Close()).To(Succeed())
 	})
 
-	Context("after the crypto handshake", func() {
-		for i := range protocol.SupportedVersions {
-			version := protocol.SupportedVersions[i]
+	for _, v := range protocol.SupportedVersions {
+		version := v
 
-			Context(fmt.Sprintf("with quic version %d", version), func() {
-				dropTests("dropping every 4th packet", 4, 1, runDropTest, version)
-				dropTests("dropping 10 packets every 100 packets", 100, 10, runDropTest, version)
+		Context(fmt.Sprintf("with QUIC version %d", version), func() {
+			Context("during the crypto handshake", func() {
+				for _, d := range directions {
+					direction := d
+
+					It(fmt.Sprintf("establishes a connection when the first packet is lost in %s direction", d), func() {
+						startProxy(func(d quicproxy.Direction, p uint64) bool {
+							return p == 1 && d.Is(direction)
+						}, version)
+						downloadHello(version)
+					})
+
+					It(fmt.Sprintf("establishes a connection when the second packet is lost in %s direction", d), func() {
+						startProxy(func(d quicproxy.Direction, p uint64) bool {
+							return p == 2 && d.Is(direction)
+						}, version)
+						downloadHello(version)
+					})
+
+					It(fmt.Sprintf("establishes a connection when 1/5 of the packets are lost in %s direction", d), func() {
+						startProxy(func(d quicproxy.Direction, p uint64) bool {
+							return d.Is(direction) && stochasticDropper(5)
+						}, version)
+						downloadHello(version)
+					})
+				}
 			})
-		}
-	})
+
+			Context("after the crypto handshake", func() {
+				for _, d := range directions {
+					direction := d
+
+					It(fmt.Sprintf("downloads a file when every 5th packet is dropped in %s direction", d), func() {
+						startProxy(func(d quicproxy.Direction, p uint64) bool {
+							return p >= 10 && d.Is(direction) && deterministicDropper(p, 5, 1)
+						}, version)
+						downloadFile(version)
+					})
+
+					It(fmt.Sprintf("downloads a file when 1/5th of all packet are dropped randomly in %s direction", d), func() {
+						startProxy(func(d quicproxy.Direction, p uint64) bool {
+							return p >= 10 && d.Is(direction) && stochasticDropper(5)
+						}, version)
+						downloadFile(version)
+					})
+
+					It(fmt.Sprintf("downloads a file when 10 packets every 100 packet are dropped in %s direction", d), func() {
+						startProxy(func(d quicproxy.Direction, p uint64) bool {
+							return p >= 10 && d.Is(direction) && deterministicDropper(p, 100, 10)
+						}, version)
+						downloadFile(version)
+					})
+				}
+			})
+		})
+	}
 })
-
-func dropTests(
-	context string,
-	interval uint64,
-	dropInARow uint64,
-	runDropTest func(dropCallback quicproxy.DropCallback, version protocol.VersionNumber),
-	version protocol.VersionNumber) {
-	Context(context, func() {
-		dropper := func(p uint64) bool {
-			if p <= 10 { // don't interfere with the crypto handshake
-				return false
-			}
-			return (p % interval) < dropInARow
-		}
-
-		It("gets a file when many outgoing packets are dropped", func() {
-			runDropTest(func(d quicproxy.Direction, p uint64) bool {
-				return d == quicproxy.DirectionOutgoing && dropper(p)
-			}, version)
-		})
-
-		It("gets a file when many incoming packets are dropped", func() {
-			runDropTest(func(d quicproxy.Direction, p uint64) bool {
-				return d == quicproxy.DirectionIncoming && dropper(p)
-			}, version)
-		})
-	})
-}
diff --git a/integrationtests/tools/proxy/proxy.go b/integrationtests/tools/proxy/proxy.go
index b8f2cf6b..a9d0d4cf 100644
--- a/integrationtests/tools/proxy/proxy.go
+++ b/integrationtests/tools/proxy/proxy.go
@@ -26,8 +26,30 @@ const (
 	DirectionIncoming Direction = iota
 	// DirectionOutgoing is the direction from the server to the client.
 	DirectionOutgoing
+	// DirectionBoth is both incoming and outgoing
+	DirectionBoth
 )
 
+func (d Direction) String() string {
+	switch d {
+	case DirectionIncoming:
+		return "incoming"
+	case DirectionOutgoing:
+		return "outgoing"
+	case DirectionBoth:
+		return "both"
+	default:
+		panic("unknown direction")
+	}
+}
+
+func (d Direction) Is(dir Direction) bool {
+	if d == DirectionBoth || dir == DirectionBoth {
+		return true
+	}
+	return d == dir
+}
+
 // DropCallback is a callback that determines which packet gets dropped.
 type DropCallback func(dir Direction, packetCount uint64) bool