diff --git a/helpers/helpers.js b/helpers/helpers.js
index d86a20d3..87c49acf 100644
--- a/helpers/helpers.js
+++ b/helpers/helpers.js
@@ -80,7 +80,7 @@ module.exports.includesSorted = function includesSorted(array, element) {
   let left = 0;
   let right = array.length - 1;
   while (left <= right) {
-    /* eslint-disable no-bitwise */
+    // eslint-disable-next-line no-bitwise
     const mid = (left + right) >> 1;
     if (array[mid] < element) {
       left = mid + 1;
diff --git a/lib/markdownlint.js b/lib/markdownlint.js
index c6849f85..0029c9d5 100644
--- a/lib/markdownlint.js
+++ b/lib/markdownlint.js
@@ -90,7 +90,9 @@ function newResults(ruleList) {
   function toString(useAlias) {
     let ruleNameToRule = null;
     const results = [];
-    Object.keys(lintResults).forEach(function forFile(file) {
+    const keys = Object.keys(lintResults);
+    keys.sort();
+    keys.forEach(function forFile(file) {
       const fileResults = lintResults[file];
       if (Array.isArray(fileResults)) {
         fileResults.forEach(function forResult(result) {
@@ -727,53 +729,98 @@ function lintInput(options, synchronous, callback) {
     md.use(...plugin);
   });
   const results = newResults(ruleList);
-  // Helper to lint the next string or file
-  /* eslint-disable consistent-return */
+  let done = false;
+  // Linting of strings is always synchronous
+  let syncItem = null;
   // eslint-disable-next-line jsdoc/require-jsdoc
-  function lintNextItem() {
-    let iterating = true;
-    let item = null;
-    // eslint-disable-next-line jsdoc/require-jsdoc
-    function lintNextItemCallback(err, result) {
-      if (err) {
-        iterating = false;
-        return callback(err);
-      }
-      results[item] = result;
-      return iterating || lintNextItem();
-    }
-    while (iterating) {
-      if ((item = stringsKeys.shift())) {
-        lintContent(
-          ruleList,
-          item,
-          strings[item] || "",
-          md,
-          config,
-          frontMatter,
-          handleRuleFailures,
-          noInlineConfig,
-          resultVersion,
-          lintNextItemCallback);
-      } else if ((item = files.shift())) {
-        iterating = synchronous;
-        lintFile(
-          ruleList,
-          item,
-          md,
-          config,
-          frontMatter,
-          handleRuleFailures,
-          noInlineConfig,
-          resultVersion,
-          synchronous,
-          lintNextItemCallback);
-      } else {
-        return callback(null, results);
-      }
+  function syncCallback(err, result) {
+    if (err) {
+      done = true;
+      return callback(err);
     }
+    results[syncItem] = result;
+    return null;
   }
-  return lintNextItem();
+  while (!done && (syncItem = stringsKeys.shift())) {
+    lintContent(
+      ruleList,
+      syncItem,
+      strings[syncItem] || "",
+      md,
+      config,
+      frontMatter,
+      handleRuleFailures,
+      noInlineConfig,
+      resultVersion,
+      syncCallback
+    );
+  }
+  if (synchronous) {
+    // Lint files synchronously
+    while (!done && (syncItem = files.shift())) {
+      lintFile(
+        ruleList,
+        syncItem,
+        md,
+        config,
+        frontMatter,
+        handleRuleFailures,
+        noInlineConfig,
+        resultVersion,
+        synchronous,
+        syncCallback
+      );
+    }
+    return done || callback(null, results);
+  }
+  // Lint files asynchronously
+  let concurrency = 0;
+  // eslint-disable-next-line jsdoc/require-jsdoc
+  function lintConcurrently() {
+    const asyncItem = files.shift();
+    if (done) {
+      // Nothing to do
+    } else if (asyncItem) {
+      concurrency++;
+      lintFile(
+        ruleList,
+        asyncItem,
+        md,
+        config,
+        frontMatter,
+        handleRuleFailures,
+        noInlineConfig,
+        resultVersion,
+        synchronous,
+        (err, result) => {
+          concurrency--;
+          if (err) {
+            done = true;
+            return callback(err);
+          }
+          results[asyncItem] = result;
+          lintConcurrently();
+          return null;
+        }
+      );
+    } else if (concurrency === 0) {
+      done = true;
+      return callback(null, results);
+    }
+    return null;
+  }
+  // Testing on a Raspberry Pi 4 Model B with an artificial 5ms file access
+  // delay suggests that a concurrency factor of 8 can eliminate the impact
+  // of that delay (i.e., total time is the same as with no delay).
+  lintConcurrently();
+  lintConcurrently();
+  lintConcurrently();
+  lintConcurrently();
+  lintConcurrently();
+  lintConcurrently();
+  lintConcurrently();
+  lintConcurrently();
+  return null;
 }
 
 /**
diff --git a/test/markdownlint-test.js b/test/markdownlint-test.js
index af14d431..3598159d 100644
--- a/test/markdownlint-test.js
+++ b/test/markdownlint-test.js
@@ -440,9 +440,6 @@ tape("resultFormattingV1", (test) => {
     test.deepEqual(actualResult, expectedResult, "Undetected issues.");
     const actualMessage = actualResult.toString();
     const expectedMessage =
-      "truncate: 1: MD021/no-multiple-space-closed-atx" +
-      " Multiple spaces inside hashes on closed atx style heading" +
-      " [Context: \"#  Multiple spa...tyle heading  #\"]\n" +
       "./test/atx_heading_spacing.md: 3: MD002/first-heading-h1" +
       " First heading should be a top level heading" +
       " [Expected: h1; Actual: h2]\n" +
@@ -457,7 +454,10 @@ tape("resultFormattingV1", (test) => {
       " [Context: \"##   Heading 3 {MD019}\"]\n" +
       "./test/first_heading_bad_atx.md: 1: MD002/first-heading-h1" +
       " First heading should be a top level heading" +
-      " [Expected: h1; Actual: h2]";
+      " [Expected: h1; Actual: h2]\n" +
+      "truncate: 1: MD021/no-multiple-space-closed-atx" +
+      " Multiple spaces inside hashes on closed atx style heading" +
+      " [Context: \"#  Multiple spa...tyle heading  #\"]";
     test.equal(actualMessage, expectedMessage, "Incorrect message.");
     test.end();
   });
@@ -535,9 +535,6 @@ tape("resultFormattingV2", (test) => {
     test.deepEqual(actualResult, expectedResult, "Undetected issues.");
     const actualMessage = actualResult.toString();
     const expectedMessage =
-      "truncate: 1: MD021/no-multiple-space-closed-atx" +
-      " Multiple spaces inside hashes on closed atx style heading" +
-      " [Context: \"#  Multiple spa...tyle heading  #\"]\n" +
       "./test/atx_heading_spacing.md: 3:" +
       " MD002/first-heading-h1/first-header-h1" +
       " First heading should be a top level heading" +
@@ -554,7 +551,10 @@ tape("resultFormattingV2", (test) => {
       "./test/first_heading_bad_atx.md: 1:" +
       " MD002/first-heading-h1/first-header-h1" +
       " First heading should be a top level heading" +
-      " [Expected: h1; Actual: h2]";
+      " [Expected: h1; Actual: h2]\n" +
+      "truncate: 1: MD021/no-multiple-space-closed-atx" +
+      " Multiple spaces inside hashes on closed atx style heading" +
+      " [Context: \"#  Multiple spa...tyle heading  #\"]";
     test.equal(actualMessage, expectedMessage, "Incorrect message.");
     test.end();
   });