diff --git a/h2quic/roundtrip.go b/h2quic/roundtrip.go
index 6b195b6f..e725ea7a 100644
--- a/h2quic/roundtrip.go
+++ b/h2quic/roundtrip.go
@@ -11,8 +11,6 @@ import (
 
 	quic "github.com/lucas-clemente/quic-go"
 
-	"runtime"
-
 	"golang.org/x/net/lex/httplex"
 )
 
@@ -93,7 +91,6 @@ func (r *RoundTripper) getClient(hostname string) http.RoundTripper {
 	defer r.mutex.Unlock()
 
 	if r.clients == nil {
-		runtime.SetFinalizer(r, finalizer)
 		r.clients = make(map[string]roundTripCloser)
 	}
 
@@ -105,10 +102,6 @@ func (r *RoundTripper) getClient(hostname string) http.RoundTripper {
 	return client
 }
 
-func finalizer(r *RoundTripper) {
-	_ = r.Close()
-}
-
 // Close closes the QUIC connections that this RoundTripper has used
 func (r *RoundTripper) Close() error {
 	r.mutex.Lock()
diff --git a/h2quic/roundtrip_test.go b/h2quic/roundtrip_test.go
index 66e3eb8a..b612d8bb 100644
--- a/h2quic/roundtrip_test.go
+++ b/h2quic/roundtrip_test.go
@@ -6,7 +6,6 @@ import (
 	"errors"
 	"io"
 	"net/http"
-	"runtime"
 	"time"
 
 	quic "github.com/lucas-clemente/quic-go"
@@ -197,16 +196,5 @@ var _ = Describe("RoundTripper", func() {
 			Expect(err).ToNot(HaveOccurred())
 			Expect(len(rt.clients)).To(BeZero())
 		})
-
-		It("runs Close when the RoundTripper is garbage collected", func() {
-			// this is set by getClient, but we can't do that while at the same time injecting the mockClient
-			runtime.SetFinalizer(rt, finalizer)
-			rt.clients = make(map[string]roundTripCloser)
-			cl := &mockClient{}
-			rt.clients["foo.bar"] = cl
-			rt = nil // lose the references to the RoundTripper, such that it can be garbage collected
-			runtime.GC()
-			Eventually(func() bool { return cl.closed }).Should(BeTrue())
-		})
 	})
 })