diff --git a/cmd/fuzz/main.go b/cmd/fuzz/main.go
index 572e0fa..c528d74 100644
--- a/cmd/fuzz/main.go
+++ b/cmd/fuzz/main.go
@@ -319,7 +319,8 @@ func startRunners(ctx context.Context, opts *Options, in <-chan string) (<-chan
 	out := make(chan response.Response)
 
 	var wg sync.WaitGroup
-	transport, err := response.NewTransport(opts.Request.Insecure, opts.Request.TLSClientKeyCertFile, opts.Request.DisableHTTP2)
+	transport, err := response.NewTransport(opts.Request.Insecure, opts.Request.TLSClientKeyCertFile,
+		opts.Request.DisableHTTP2, opts.Threads)
 	if err != nil {
 		return nil, err
 	}
diff --git a/cmd/test/main.go b/cmd/test/main.go
index 0964fe8..2320c2f 100644
--- a/cmd/test/main.go
+++ b/cmd/test/main.go
@@ -115,7 +115,8 @@ func run(ctx context.Context, g *errgroup.Group, opts *Options, args []string) e
 
 	output := make(chan response.Response, 1)
 
-	tr, err := response.NewTransport(opts.Request.Insecure, opts.Request.TLSClientKeyCertFile, opts.Request.DisableHTTP2)
+	tr, err := response.NewTransport(opts.Request.Insecure, opts.Request.TLSClientKeyCertFile,
+		opts.Request.DisableHTTP2, 1)
 	if err != nil {
 		return err
 	}
diff --git a/response/runner.go b/response/runner.go
index 1f63fa1..72e549a 100644
--- a/response/runner.go
+++ b/response/runner.go
@@ -34,7 +34,8 @@ type Runner struct {
 const DefaultBodyBufferSize = 5 * 1024 * 1024
 
 // NewTransport creates a new shared transport for clients to use.
-func NewTransport(insecure bool, TLSClientCertKeyFilename string, disableHTTP2 bool) (*http.Transport, error) {
+func NewTransport(insecure bool, TLSClientCertKeyFilename string,
+	disableHTTP2 bool, concurrentRequests int) (*http.Transport, error) {
 	// for timeouts, see
 	// https://blog.cloudflare.com/the-complete-guide-to-golang-net-http-timeouts/
 	tr := &http.Transport{
@@ -48,6 +49,8 @@ func NewTransport(insecure bool, TLSClientCertKeyFilename string, disableHTTP2 b
 		ExpectContinueTimeout: 1 * time.Second,
 		IdleConnTimeout:       15 * time.Second,
 		TLSClientConfig:       &tls.Config{},
+		MaxIdleConns:          concurrentRequests,
+		MaxIdleConnsPerHost:   concurrentRequests,
 	}
 
 	if insecure {