diff --git a/lib/dispatcher/client-h2.js b/lib/dispatcher/client-h2.js
index d4dc681f94a..9d070958135 100644
--- a/lib/dispatcher/client-h2.js
+++ b/lib/dispatcher/client-h2.js
@@ -538,25 +538,17 @@ function shouldSendContentLength (method) {
   return method !== 'GET' && method !== 'HEAD' && method !== 'OPTIONS' && method !== 'TRACE' && method !== 'CONNECT'
 }
 
-function writeH2 (client, request) {
-  const requestTimeout = request.bodyTimeout ?? client[kBodyTimeout]
-  const session = client[kHTTP2Session]
-  const { method, path, host, upgrade, expectContinue, signal, protocol, headers: reqHeaders } = request
-  let { body } = request
-
-  if (upgrade != null && upgrade !== 'websocket') {
-    util.errorRequest(client, request, new InvalidArgumentError(`Custom upgrade "${upgrade}" not supported over HTTP/2`))
-    return false
-  }
-
+function buildRequestHeaders (reqHeaders) {
   const headers = {}
+
   for (let n = 0; n < reqHeaders.length; n += 2) {
     const key = reqHeaders[n + 0]
     const val = reqHeaders[n + 1]
+    const current = headers[key]
 
     if (key === 'cookie') {
-      if (headers[key] != null) {
-        headers[key] = Array.isArray(headers[key]) ? (headers[key].push(val), headers[key]) : [headers[key], val]
+      if (current != null) {
+        headers[key] = Array.isArray(current) ? (current.push(val), current) : [current, val]
       } else {
         headers[key] = val
       }
@@ -564,21 +556,32 @@ function writeH2 (client, request) {
       continue
     }
 
-    if (Array.isArray(val)) {
-      for (let i = 0; i < val.length; i++) {
-        if (headers[key]) {
-          headers[key] += `, ${val[i]}`
-        } else {
-          headers[key] = val[i]
-        }
-      }
-    } else if (headers[key]) {
-      headers[key] += `, ${val}`
-    } else {
-      headers[key] = val
+    if (typeof val === 'string') {
+      headers[key] = current ? `${current}, ${val}` : val
+      continue
     }
+
+    for (let i = 0; i < val.length; i++) {
+      headers[key] = headers[key] ? `${headers[key]}, ${val[i]}` : val[i]
+    }
+  }
+
+  return headers
+}
+
+function writeH2 (client, request) {
+  const requestTimeout = request.bodyTimeout ?? client[kBodyTimeout]
+  const session = client[kHTTP2Session]
+  const { method, path, host, upgrade, expectContinue, signal, protocol, headers: reqHeaders } = request
+  let { body } = request
+
+  if (upgrade != null && upgrade !== 'websocket') {
+    util.errorRequest(client, request, new InvalidArgumentError(`Custom upgrade "${upgrade}" not supported over HTTP/2`))
+    return false
   }
 
+  const headers = buildRequestHeaders(reqHeaders)
+
   /** @type {import('node:http2').ClientHttp2Stream} */
   let stream = null