diff --git a/go.mod b/go.mod
index 721666a..a3991b2 100644
--- a/go.mod
+++ b/go.mod
@@ -6,7 +6,7 @@ require (
 	github.com/caddyserver/caddy/v2 v2.8.4
 	github.com/caddyserver/certmagic v0.21.3
 	github.com/google/go-cmp v0.6.0
-	github.com/tailscale/tscert v0.0.0-20240517230440-bbccfbf48933
+	github.com/tailscale/tscert v0.0.0-20240607232451-34704dbdb4b3
 	go.uber.org/zap v1.27.0
 	tailscale.com v1.67.0-pre.0.20240602211424-42cfbf427c67
 )
diff --git a/go.sum b/go.sum
index d77dd7f..d583725 100644
--- a/go.sum
+++ b/go.sum
@@ -521,8 +521,8 @@ github.com/tailscale/netlink v1.1.1-0.20211101221916-cabfb018fe85 h1:zrsUcqrG2uQ
 github.com/tailscale/netlink v1.1.1-0.20211101221916-cabfb018fe85/go.mod h1:NzVQi3Mleb+qzq8VmcWpSkcSYxXIg0DkI6XDzpVkhJ0=
 github.com/tailscale/peercred v0.0.0-20240214030740-b535050b2aa4 h1:Gz0rz40FvFVLTBk/K8UNAenb36EbDSnh+q7Z9ldcC8w=
 github.com/tailscale/peercred v0.0.0-20240214030740-b535050b2aa4/go.mod h1:phI29ccmHQBc+wvroosENp1IF9195449VDnFDhJ4rJU=
-github.com/tailscale/tscert v0.0.0-20240517230440-bbccfbf48933 h1:pV0H+XIvFoP7pl1MRtyPXh5hqoxB5I7snOtTHgrn6HU=
-github.com/tailscale/tscert v0.0.0-20240517230440-bbccfbf48933/go.mod h1:kNGUQ3VESx3VZwRwA9MSCUegIl6+saPL8Noq82ozCaU=
+github.com/tailscale/tscert v0.0.0-20240607232451-34704dbdb4b3 h1:KKyPUIj4xlNYCryHDjvaQs92jYaEyYrmLAC9Ip4S6js=
+github.com/tailscale/tscert v0.0.0-20240607232451-34704dbdb4b3/go.mod h1:kNGUQ3VESx3VZwRwA9MSCUegIl6+saPL8Noq82ozCaU=
 github.com/tailscale/web-client-prebuilt v0.0.0-20240226180453-5db17b287bf1 h1:tdUdyPqJ0C97SJfjB9tW6EylTtreyee9C44de+UBG0g=
 github.com/tailscale/web-client-prebuilt v0.0.0-20240226180453-5db17b287bf1/go.mod h1:agQPE6y6ldqCOui2gkIh7ZMztTkIQKH049tv8siLuNQ=
 github.com/tailscale/wf v0.0.0-20240214030419-6fbb0a674ee6 h1:l10Gi6w9jxvinoiq15g8OToDdASBni4CyJOdHY1Hr8M=
diff --git a/module.go b/module.go
index 778ab70..7ed0f0c 100644
--- a/module.go
+++ b/module.go
@@ -12,17 +12,20 @@ import (
 	"crypto/tls"
 	"fmt"
 	"net"
+	"net/http"
 	"net/netip"
 	"os"
 	"path/filepath"
 	"strconv"
 	"strings"
+	"sync"
 
 	"github.com/caddyserver/caddy/v2"
 	"github.com/caddyserver/caddy/v2/modules/caddyhttp"
 	"github.com/caddyserver/certmagic"
 	"github.com/tailscale/tscert"
 	"go.uber.org/zap"
+	"tailscale.com/client/tailscale"
 	"tailscale.com/hostinfo"
 	"tailscale.com/tsnet"
 )
@@ -34,9 +37,9 @@ func init() {
 	caddyhttp.RegisterNetworkHTTP3("tailscale", "tailscale/udp")
 
 	// Caddy uses tscert to get certificates for Tailscale hostnames.
-	// Update the tscert dialer to dial the LocalAPI of the correct tsnet node,
-	// rather than just always dialing the local tailscaled.
-	tscert.TailscaledDialer = localAPIDialer
+	// Update the tscert transport to send requests to the correct tsnet server,
+	// rather than just always connecting to the local machine's tailscaled.
+	tscert.TailscaledTransport = &tsnetMuxTransport{}
 	hostinfo.SetApp("caddy")
 }
 
@@ -317,40 +320,53 @@ func (t *tsnetServerListener) Close() error {
 	return err
 }
 
-// localAPIDialer finds the node that matches the requested certificate in ctx
-// and dials that node's local API.
-// If no matching node is found, the default dialer is used,
-// which tries to connect to a local tailscaled on the machine.
-func localAPIDialer(ctx context.Context, network, addr string) (net.Conn, error) {
-	if addr != "local-tailscaled.sock:80" {
-		return nil, fmt.Errorf("unexpected URL address %q", addr)
-	}
+// tsnetMuxTransport is an [http.RoundTripper] that sends requests to the LocalAPI
+// for the tsnet server that matches the ClientHelloInfo server name.
+// If no tsnet server matches, a default Transport is used.
+type tsnetMuxTransport struct {
+	defaultTransport     *http.Transport
+	defaultTransportOnce sync.Once
+}
+
+func (t *tsnetMuxTransport) RoundTrip(req *http.Request) (*http.Response, error) {
+	ctx := req.Context()
+	var rt http.RoundTripper
 
 	clientHello, ok := ctx.Value(certmagic.ClientHelloInfoCtxKey).(*tls.ClientHelloInfo)
-	if !ok || clientHello == nil {
-		return tscert.DialLocalAPI(ctx, network, addr)
-	}
-
-	var tn *tailscaleNode
-	nodes.Range(func(key, value any) bool {
-		if n, ok := value.(*tailscaleNode); ok && n != nil {
-			for _, d := range n.CertDomains() {
-				// Tailscale doesn't do wildcard certs, but caddy uses MatchWildcard
-				// for the built-in Tailscale cert manager, so we do so here as well.
-				if certmagic.MatchWildcard(clientHello.ServerName, d) {
-					tn = n
-					return false
+	if ok && clientHello != nil {
+		nodes.Range(func(key, value any) bool {
+			if n, ok := value.(*tailscaleNode); ok && n != nil {
+				for _, d := range n.CertDomains() {
+					// Tailscale doesn't do wildcard certs, but caddy uses MatchWildcard
+					// for the built-in Tailscale cert manager, so we do so here as well.
+					if certmagic.MatchWildcard(clientHello.ServerName, d) {
+						if lc, err := n.LocalClient(); err == nil {
+							rt = &localAPITransport{lc}
+						}
+						return false
+					}
 				}
 			}
-		}
-		return true
-	})
+			return true
+		})
+	}
 
-	if tn != nil {
-		if lc, err := tn.LocalClient(); err == nil {
-			return lc.Dial(ctx, network, addr)
-		}
+	if rt == nil {
+		t.defaultTransportOnce.Do(func() {
+			t.defaultTransport = &http.Transport{
+				DialContext: tscert.TailscaledDialer,
+			}
+		})
+		rt = t.defaultTransport
 	}
+	return rt.RoundTrip(req)
+}
+
+// localAPITransport is an [http.RoundTripper] that sends requests to a [tailscale.LocalClient]'s LocalAPI.
+type localAPITransport struct {
+	*tailscale.LocalClient
+}
 
-	return tscert.DialLocalAPI(ctx, network, addr)
+func (t *localAPITransport) RoundTrip(req *http.Request) (*http.Response, error) {
+	return t.DoLocalRequest(req)
 }