diff --git a/lib/fetch/request.js b/lib/fetch/request.js
index 5e1114636dc..3b813aa77df 100644
--- a/lib/fetch/request.js
+++ b/lib/fetch/request.js
@@ -184,8 +184,10 @@ class Request {
       urlList: [...request.urlList]
     })
 
+    const initHasKey = Object.keys(init).length !== 0
+
     // 13. If init is not empty, then:
-    if (Object.keys(init).length > 0) {
+    if (initHasKey) {
       // 1. If request’s mode is "navigate", then set it to "same-origin".
       if (request.mode === 'navigate') {
         request.mode = 'same-origin'
@@ -416,25 +418,25 @@ class Request {
     }
 
     // 32. If init is not empty, then:
-    if (Object.keys(init).length !== 0) {
+    if (initHasKey) {
+      /** @type {HeadersList} */
+      const headersList = this[kHeaders][kHeadersList]
       // 1. Let headers be a copy of this’s headers and its associated header
       // list.
-      let headers = new Headers(this[kHeaders])
-
       // 2. If init["headers"] exists, then set headers to init["headers"].
-      if (init.headers !== undefined) {
-        headers = init.headers
-      }
+      const headers = init.headers !== undefined ? init.headers : new HeadersList(headersList)
 
       // 3. Empty this’s headers’s header list.
-      this[kHeaders][kHeadersList].clear()
+      headersList.clear()
 
       // 4. If headers is a Headers object, then for each header in its header
       // list, append header’s name/header’s value to this’s headers.
-      if (headers.constructor.name === 'Headers') {
+      if (headers instanceof HeadersList) {
         for (const [key, val] of headers) {
-          this[kHeaders].append(key, val)
+          headersList.append(key, val)
         }
+        // Note: Copy the `set-cookie` meta-data.
+        headersList.cookies = headers.cookies
       } else {
         // 5. Otherwise, fill this’s headers with headers.
         fillHeaders(this[kHeaders], headers)