diff --git a/lib/core/util.js b/lib/core/util.js
index d8833c01e7c..5f5949c330e 100644
--- a/lib/core/util.js
+++ b/lib/core/util.js
@@ -928,6 +928,44 @@ const normalizedMethodRecords = {
 Object.setPrototypeOf(normalizedMethodRecordsBase, null)
 Object.setPrototypeOf(normalizedMethodRecords, null)
 
+/**
+ * @param {Record<string, string | string[]> | Iterable<[string, string]> | string[] | null | undefined} headers
+ * @returns {Record<string, string[] | string>}
+ */
+function normalizeHeaders (headers) {
+  const normalized = {}
+  const src = headers
+
+  if (typeof src !== 'object' || src === null) return normalized
+
+  if (Array.isArray(src)) {
+    for (let i = 0; i < src.length; i += 2) {
+      normalized[src[i]] = src[i + 1]
+    }
+    return normalized
+  }
+
+  if (typeof src[Symbol.iterator] === 'function') {
+    const errMsg = 'headers is not a valid header map'
+    for (const s of src) {
+      if (!Array.isArray(s)) throw new InvalidArgumentError(errMsg)
+      const [key, val] = s
+      if (typeof key !== 'string' || typeof val !== 'string') {
+        throw new InvalidArgumentError(errMsg)
+      }
+      const lowerKey = headerNameLowerCasedRecord[key] ?? key.toLowerCase()
+      normalized[lowerKey] = val
+    }
+    return normalized
+  }
+
+  for (const key of Object.keys(src)) {
+    const lowerKey = headerNameLowerCasedRecord[key] ?? key.toLowerCase()
+    normalized[lowerKey] = src[key]
+  }
+  return normalized
+}
+
 module.exports = {
   kEnumerableProperty,
   isDisturbed,
@@ -963,6 +1001,7 @@ module.exports = {
   isValidHeaderValue,
   isTokenCharCode,
   parseRangeHeader,
+  normalizeHeaders,
   normalizedMethodRecordsBase,
   normalizedMethodRecords,
   isValidPort,
diff --git a/lib/interceptor/cache.js b/lib/interceptor/cache.js
index d561d4572cc..f1ef18e357e 100644
--- a/lib/interceptor/cache.js
+++ b/lib/interceptor/cache.js
@@ -6,7 +6,8 @@ const util = require('../core/util')
 const CacheHandler = require('../handler/cache-handler')
 const MemoryCacheStore = require('../cache/memory-cache-store')
 const CacheRevalidationHandler = require('../handler/cache-revalidation-handler')
-const { assertCacheStore, assertCacheMethods, makeCacheKey, normalizeHeaders, parseCacheControlHeader } = require('../util/cache.js')
+const { assertCacheStore, assertCacheMethods, makeCacheKey, parseCacheControlHeader } = require('../util/cache.js')
+const { normalizeHeaders } = require('../core/util.js')
 const { AbortError } = require('../core/errors.js')
 
 /**
@@ -387,7 +388,7 @@ module.exports = (opts = {}) => {
 
       opts = {
         ...opts,
-        headers: normalizeHeaders(opts)
+        headers: normalizeHeaders(opts.headers)
       }
 
       const reqCacheControl = opts.headers?.['cache-control']
diff --git a/lib/interceptor/dns.js b/lib/interceptor/dns.js
index 38287607143..d97484d7efc 100644
--- a/lib/interceptor/dns.js
+++ b/lib/interceptor/dns.js
@@ -4,6 +4,7 @@ const { lookup } = require('node:dns')
 const DecoratorHandler = require('../handler/decorator-handler')
 const { InvalidArgumentError, InformationalError } = require('../core/errors')
 const maxInt = Math.pow(2, 31) - 1
+const { normalizeHeaders } = require('../core/util.js')
 
 class DNSInstance {
   #maxTTL = 0
@@ -411,10 +412,7 @@ module.exports = interceptorOpts => {
           ...origDispatchOpts,
           servername: origin.hostname, // For SNI on TLS
           origin: newOrigin.origin,
-          headers: {
-            host: origin.host,
-            ...origDispatchOpts.headers
-          }
+          headers: { host: origin.host, ...normalizeHeaders(origDispatchOpts.headers) }
         }
 
         dispatch(
diff --git a/lib/util/cache.js b/lib/util/cache.js
index a05530f783b..95f701c81a7 100644
--- a/lib/util/cache.js
+++ b/lib/util/cache.js
@@ -29,39 +29,6 @@ function makeCacheKey (opts) {
   }
 }
 
-/**
- * @param {Record<string, string[] | string>}
- * @returns {Record<string, string[] | string>}
- */
-function normalizeHeaders (opts) {
-  let headers
-  if (opts.headers == null) {
-    headers = {}
-  } else if (typeof opts.headers[Symbol.iterator] === 'function') {
-    headers = {}
-    for (const x of opts.headers) {
-      if (!Array.isArray(x)) {
-        throw new Error('opts.headers is not a valid header map')
-      }
-      const [key, val] = x
-      if (typeof key !== 'string' || typeof val !== 'string') {
-        throw new Error('opts.headers is not a valid header map')
-      }
-      headers[key.toLowerCase()] = val
-    }
-  } else if (typeof opts.headers === 'object') {
-    headers = {}
-
-    for (const key of Object.keys(opts.headers)) {
-      headers[key.toLowerCase()] = opts.headers[key]
-    }
-  } else {
-    throw new Error('opts.headers is not an object')
-  }
-
-  return headers
-}
-
 /**
  * @param {any} key
  */
@@ -366,7 +333,6 @@ function assertCacheMethods (methods, name = 'CacheMethods') {
 
 module.exports = {
   makeCacheKey,
-  normalizeHeaders,
   assertCacheKey,
   assertCacheValue,
   parseCacheControlHeader,
diff --git a/test/interceptors/dns.js b/test/interceptors/dns.js
index 3ee48c20973..950417e3bc1 100644
--- a/test/interceptors/dns.js
+++ b/test/interceptors/dns.js
@@ -1936,3 +1936,54 @@ test('#3951 - Should handle lookup errors correctly', async t => {
     origin: 'http://localhost'
   }), new Error('lookup error'))
 })
+
+test('Various (parameterized) header shapes should work with DNS interceptor', async t => {
+  const server = createServer({ joinDuplicateHeaders: true })
+  server.on('request', (req, res) => {
+    t.equal(req.headers.foo, 'bar')
+    t.equal(typeof req.headers['0'], 'undefined')
+    t.match(req.headers.host, /^localhost:\d+$/)
+    res.end('ok')
+  })
+
+  server.listen(0)
+  await once(server, 'listening')
+
+  const origin = `http://localhost:${server.address().port}`
+
+  const cases = [
+    {
+      name: 'flat array',
+      headers: ['foo', 'bar']
+    },
+    {
+      name: 'record',
+      headers: { foo: 'bar' }
+    },
+    {
+      name: 'record with multi-value',
+      headers: { foo: ['bar'] }
+    },
+    {
+      name: 'iterable (map) object',
+      headers: new Map([['foo', 'bar']])
+    },
+    {
+      name: 'iterable (set) object',
+      headers: new Set([['foo', 'bar']])
+    }
+  ]
+
+  t = tspl(t, { plan: cases.length * 4 })
+
+  for (const c of cases) {
+    const agent = new Agent().compose(dns())
+    const r = await agent.request({ origin, path: '/', method: 'GET', headers: c.headers })
+    t.equal(r.statusCode, 200, c.name)
+    await r.body.text()
+    await agent.close()
+  }
+
+  server.close()
+  await once(server, 'close')
+})