diff --git a/lib/copy/copy.js b/lib/copy/copy.js
index 47fd9836..40652f47 100644
--- a/lib/copy/copy.js
+++ b/lib/copy/copy.js
@@ -6,6 +6,7 @@ const { mkdirs } = require('../mkdirs')
 const { pathExists } = require('../path-exists')
 const { utimesMillis } = require('../util/utimes')
 const stat = require('../util/stat')
+const { asyncIteratorConcurrentProcess } = require('../util/async')
 
 async function copy (src, dest, opts = {}) {
   if (typeof opts === 'function') {
@@ -113,28 +114,20 @@ async function onDir (srcStat, destStat, src, dest, opts) {
     await fs.mkdir(dest)
   }
 
-  const promises = []
-
-  // loop through the files in the current directory to copy everything
-  for await (const item of await fs.opendir(src)) {
+  // iterate through the files in the current directory to copy everything
+  await asyncIteratorConcurrentProcess(await fs.opendir(src), async (item) => {
     const srcItem = path.join(src, item.name)
     const destItem = path.join(dest, item.name)
 
-    promises.push(
-      runFilter(srcItem, destItem, opts).then(include => {
-        if (include) {
-          // only copy the item if it matches the filter function
-          return stat.checkPaths(srcItem, destItem, 'copy', opts).then(({ destStat }) => {
-            // If the item is a copyable file, `getStatsAndPerformCopy` will copy it
-            // If the item is a directory, `getStatsAndPerformCopy` will call `onDir` recursively
-            return getStatsAndPerformCopy(destStat, srcItem, destItem, opts)
-          })
-        }
-      })
-    )
-  }
-
-  await Promise.all(promises)
+    const include = await runFilter(srcItem, destItem, opts)
+    // only copy the item if it matches the filter function
+    if (include) {
+      const { destStat } = await stat.checkPaths(srcItem, destItem, 'copy', opts)
+      // If the item is a copyable file, `getStatsAndPerformCopy` will copy it
+      // If the item is a directory, `getStatsAndPerformCopy` will call `onDir` recursively
+      await getStatsAndPerformCopy(destStat, srcItem, destItem, opts)
+    }
+  })
 
   if (!destStat) {
     await fs.chmod(dest, srcStat.mode)
diff --git a/lib/util/async.js b/lib/util/async.js
new file mode 100644
index 00000000..3f6288df
--- /dev/null
+++ b/lib/util/async.js
@@ -0,0 +1,29 @@
+'use strict'
+
+// https://github.com/jprichardson/node-fs-extra/issues/1056
+// Performing parallel operations on each item of an async iterator is
+// surprisingly hard; you need to have handlers in place to avoid getting an
+// UnhandledPromiseRejectionWarning.
+// NOTE: This function does not presently handle return values, only errors
+async function asyncIteratorConcurrentProcess (iterator, fn) {
+  const promises = []
+  for await (const item of iterator) {
+    promises.push(
+      fn(item).then(
+        () => null,
+        (err) => err ?? new Error('unknown error')
+      )
+    )
+  }
+  await Promise.all(
+    promises.map((promise) =>
+      promise.then((possibleErr) => {
+        if (possibleErr !== null) throw possibleErr
+      })
+    )
+  )
+}
+
+module.exports = {
+  asyncIteratorConcurrentProcess
+}