diff --git a/test/client-node-max-header-size.js b/test/client-node-max-header-size.js
index 227f6705084..379c5e6970a 100644
--- a/test/client-node-max-header-size.js
+++ b/test/client-node-max-header-size.js
@@ -1,21 +1,44 @@
 'use strict'
 
-const { execSync } = require('node:child_process')
-const { throws, doesNotThrow } = require('node:assert')
-const { test } = require('node:test')
-
-const command = 'node -e "require(\'.\').request(\'https://httpbin.org/get\')"'
-
-test("respect Node.js' --max-http-header-size", () => {
-  throws(
-    () => execSync(`${command} --max-http-header-size=1`, { stdio: 'pipe' }),
-    /UND_ERR_HEADERS_OVERFLOW/,
-    'max-http-header-size=1 should throw'
-  )
-
-  doesNotThrow(
-    () => execSync(command),
-    /UND_ERR_HEADERS_OVERFLOW/,
-    'default max-http-header-size should not throw'
-  )
+const { tspl } = require('@matteo.collina/tspl')
+const { once } = require('node:events')
+const { exec } = require('node:child_process')
+const { test, before, after, describe } = require('node:test')
+const { createServer } = require('node:http')
+
+describe("Node.js' --max-http-header-size cli option", () => {
+  let server
+
+  before(async () => {
+    server = createServer((req, res) => {
+      res.writeHead(200, 'OK', {
+        'Content-Length': 2
+      })
+      res.write('OK')
+      res.end()
+    }).listen(0)
+
+    await once(server, 'listening')
+  })
+
+  after(() => server.close())
+
+  test("respect Node.js' --max-http-header-size", async (t) => {
+    t = tspl(t, { plan: 6 })
+    const command = 'node -e "require(\'.\').request(\'http://localhost:' + server.address().port + '\')"'
+
+    exec(`${command} --max-http-header-size=1`, { stdio: 'pipe' }, (err, stdout, stderr) => {
+      t.strictEqual(err.code, 1)
+      t.strictEqual(stdout, '')
+      t.match(stderr, /UND_ERR_HEADERS_OVERFLOW/, '--max-http-header-size=1 should throw')
+    })
+
+    exec(command, { stdio: 'pipe' }, (err, stdout, stderr) => {
+      t.ifError(err)
+      t.strictEqual(stdout, '')
+      t.strictEqual(stderr, '', 'default max-http-header-size should not throw')
+    })
+
+    await t.completed
+  })
 })
diff --git a/test/connect-timeout.js b/test/connect-timeout.js
index d8ff177504c..1378de82cf5 100644
--- a/test/connect-timeout.js
+++ b/test/connect-timeout.js
@@ -16,7 +16,7 @@ describe('prioritize socket errors over timeouts', () => {
   client.request({ method: 'GET', path: '/foobar' })
     .then(() => t.fail())
     .catch((err) => {
-      t.strictEqual(err.code, 'ENOTFOUND')
+      t.strictEqual(['ENOTFOUND', 'EAI_AGAIN'].includes(err.code), true)
     })
 
   // block for 1s which is enough for the dns lookup to complete and TO to fire
diff --git a/test/issue-1670.js b/test/issue-1670.js
index 7a0cda32669..26904d4da8f 100644
--- a/test/issue-1670.js
+++ b/test/issue-1670.js
@@ -3,7 +3,7 @@
 const { test } = require('node:test')
 const { request } = require('..')
 
-test('https://github.com/mcollina/undici/issues/810', async () => {
+test('https://github.com/mcollina/undici/issues/1670', async () => {
   const { body } = await request('https://api.github.com/user/emails')
 
   await body.text()