diff --git a/lib/index.js b/lib/index.js
index 82fb3e5..f081c93 100644
--- a/lib/index.js
+++ b/lib/index.js
@@ -12,9 +12,13 @@
 import {deadOrAlive} from 'dead-or-alive'
 import {ok as assert} from 'devlop'
 import isOnline from 'is-online'
+import pAll from 'p-all'
+import pLimit from 'p-limit'
 import {lintRule} from 'unified-lint-rule'
 import {visit} from 'unist-util-visit'
 
+const limit = pLimit(1)
+
 /** @type {Readonly<Options>} */
 const emptyOptions = {}
 const defaultSkipUrlPatterns = [/^(?!https?)/i]
@@ -55,124 +59,133 @@ export default remarkLintNoDeadUrls
  *   Nothing.
  */
 async function rule(tree, file, options) {
-  /** @type {Map<string, Array<Resources>>} */
-  const nodesByUrl = new Map()
-  const online = await isOnline()
-  const settings = options || emptyOptions
-  const skipUrlPatterns = settings.skipUrlPatterns
-    ? settings.skipUrlPatterns.map(function (d) {
-        return typeof d === 'string' ? new RegExp(d) : d
-      })
-    : [...defaultSkipUrlPatterns]
-
-  if (settings.skipLocalhost) {
-    skipUrlPatterns.push(/^(https?:\/\/)(localhost|127\.0\.0\.1)(:\d+)?/)
-  }
-
-  /* c8 ignore next 9 -- difficult to test */
-  if (!online) {
-    if (!settings.skipOffline) {
-      file.info(
-        'Unexpected offline connection, expected either an online connection or `skipOffline: true`'
-      )
-    }
+  // Operate one file at a time.
+  // Otherwise we’d send out tons of requests at a time for say 10 files.
+  await limit(async function () {
+    /** @type {Map<string, Array<Resources>>} */
+    const nodesByUrl = new Map()
+    const online = await isOnline()
+    const settings = options || emptyOptions
+    const skipUrlPatterns = settings.skipUrlPatterns
+      ? settings.skipUrlPatterns.map(function (d) {
+          return typeof d === 'string' ? new RegExp(d) : d
+        })
+      : [...defaultSkipUrlPatterns]
 
-    return
-  }
-
-  const meta = /** @type {Record<string, unknown> | undefined} */ (
-    file.data.meta
-  )
-
-  const from =
-    settings.from ||
-    (meta &&
-    typeof meta.origin === 'string' &&
-    typeof meta.pathname === 'string'
-      ? new URL(meta.pathname, meta.origin).href
-      : undefined)
-
-  const deadOrAliveOptions = {
-    ...settings.deadOrAliveOptions,
-    findUrls: false
-  }
-
-  visit(tree, function (node) {
-    if ('url' in node && typeof node.url === 'string') {
-      const value = node.url
-      const colon = value.indexOf(':')
-      const questionMark = value.indexOf('?')
-      const numberSign = value.indexOf('#')
-      const slash = value.indexOf('/')
-      let relativeToSomething = false
-
-      if (
-        // If there is no protocol, it’s relative.
-        colon < 0 ||
-        // If the first colon is after a `?`, `#`, or `/`, it’s not a protocol.
-        (slash > -1 && colon > slash) ||
-        (questionMark > -1 && colon > questionMark) ||
-        (numberSign > -1 && colon > numberSign)
-      ) {
-        relativeToSomething = true
-      }
+    if (settings.skipLocalhost) {
+      skipUrlPatterns.push(/^(https?:\/\/)(localhost|127\.0\.0\.1)(:\d+)?/)
+    }
 
-      // We can only check URLs relative to something if `from` is passed.
-      if (relativeToSomething && !from) {
-        return
+    /* c8 ignore next 9 -- difficult to test */
+    if (!online) {
+      if (!settings.skipOffline) {
+        file.info(
+          'Unexpected offline connection, expected either an online connection or `skipOffline: true`'
+        )
       }
 
-      const url = new URL(value, from).href
+      return
+    }
 
-      if (
-        skipUrlPatterns.some(function (skipPattern) {
-          return skipPattern.test(url)
-        })
-      ) {
-        return
-      }
+    const meta = /** @type {Record<string, unknown> | undefined} */ (
+      file.data.meta
+    )
+
+    const from =
+      settings.from ||
+      (meta &&
+      typeof meta.origin === 'string' &&
+      typeof meta.pathname === 'string'
+        ? new URL(meta.pathname, meta.origin).href
+        : undefined)
+
+    const deadOrAliveOptions = {
+      ...settings.deadOrAliveOptions,
+      findUrls: false
+    }
 
-      let list = nodesByUrl.get(url)
+    visit(tree, function (node) {
+      if ('url' in node && typeof node.url === 'string') {
+        const value = node.url
+        const colon = value.indexOf(':')
+        const questionMark = value.indexOf('?')
+        const numberSign = value.indexOf('#')
+        const slash = value.indexOf('/')
+        let relativeToSomething = false
+
+        if (
+          // If there is no protocol, it’s relative.
+          colon < 0 ||
+          // If the first colon is after a `?`, `#`, or `/`, it’s not a protocol.
+          (slash > -1 && colon > slash) ||
+          (questionMark > -1 && colon > questionMark) ||
+          (numberSign > -1 && colon > numberSign)
+        ) {
+          relativeToSomething = true
+        }
 
-      if (!list) {
-        list = []
-        nodesByUrl.set(url, list)
-      }
+        // We can only check URLs relative to something if `from` is passed.
+        if (relativeToSomething && !from) {
+          return
+        }
 
-      list.push(node)
-    }
-  })
+        const url = new URL(value, from).href
 
-  const urls = [...nodesByUrl.keys()]
-
-  await Promise.all(
-    urls.map(async function (url) {
-      const nodes = nodesByUrl.get(url)
-      assert(nodes)
-      const result = await deadOrAlive(url, deadOrAliveOptions)
-
-      for (const node of nodes) {
-        for (const message of result.messages) {
-          const product = file.message(
-            'Unexpected dead URL `' + url + '`, expected live URL',
-            {ancestors: [node], cause: message, place: node.position}
-          )
-          product.fatal = message.fatal
+        if (
+          skipUrlPatterns.some(function (skipPattern) {
+            return skipPattern.test(url)
+          })
+        ) {
+          return
         }
 
-        if (result.status === 'alive' && new URL(url).href !== result.url) {
-          const message = file.message(
-            'Unexpected redirecting URL `' +
-              url +
-              '`, expected final URL `' +
-              result.url +
-              '`',
-            {ancestors: [node], place: node.position}
-          )
-          message.actual = url
-          message.expected = [result.url]
+        let list = nodesByUrl.get(url)
+
+        if (!list) {
+          list = []
+          nodesByUrl.set(url, list)
         }
+
+        list.push(node)
       }
     })
-  )
+
+    const urls = [...nodesByUrl.keys()]
+
+    await pAll(
+      urls.map(function (url) {
+        return async function () {
+          const nodes = nodesByUrl.get(url)
+          assert(nodes)
+
+          const result = await deadOrAlive(url, deadOrAliveOptions)
+
+          for (const node of nodes) {
+            for (const message of result.messages) {
+              const product = file.message(
+                'Unexpected dead URL `' + url + '`, expected live URL',
+                {ancestors: [node], cause: message, place: node.position}
+              )
+              product.fatal = message.fatal
+            }
+
+            if (result.status === 'alive' && new URL(url).href !== result.url) {
+              const message = file.message(
+                'Unexpected redirecting URL `' +
+                  url +
+                  '`, expected final URL `' +
+                  result.url +
+                  '`',
+                {ancestors: [node], place: node.position}
+              )
+              message.actual = url
+              message.expected = [result.url]
+            }
+          }
+        }
+      }),
+      // Operate on 10 URLs at a time.
+      {concurrency: 10}
+    )
+  })
 }
diff --git a/package.json b/package.json
index a6a03f0..38b5e6e 100644
--- a/package.json
+++ b/package.json
@@ -36,6 +36,8 @@
     "dead-or-alive": "^1.0.0",
     "devlop": "^1.0.0",
     "is-online": "^11.0.0",
+    "p-all": "^5.0.0",
+    "p-limit": "^6.0.0",
     "unified-lint-rule": "^3.0.0",
     "unist-util-visit": "^5.0.0",
     "vfile": "^6.0.0",