diff --git a/index.js b/index.js
index 8ddc89b..c3ae087 100644
--- a/index.js
+++ b/index.js
@@ -15,8 +15,9 @@ var PLACE_HOLDER_REGEXP = new RegExp('(\\\\)?"@__(F|R|D|M|S|A|U|I|B|L)-' + UID +
 // call could start past a `[native code]` match and wrongly report a native
 // function as safe to serialize.
 var IS_NATIVE_CODE_REGEXP = /\{\s*\[native code\]\s*\}/;
-var IS_PURE_FUNCTION = /function.*?\(/;
-var IS_ARROW_FUNCTION = /.*?=>.*?/;
+// Classify the outer function, not a declaration or arrow inside its body.
+var IS_PURE_FUNCTION = /^(?:async(?:\s|\/\*[\s\S]*?\*\/|\/\/[^\n]*\n)+)?function\b/;
+var IS_ARROW_FUNCTION = /^(?:async(?:\s|\/\*[\s\S]*?\*\/|\/\/[^\n]*\n)+)?(?:\([\s\S]*?\)|[^\s()]+)\s*=>/;
 var UNSAFE_CHARS_REGEXP   = /[<>\/\u2028\u2029]/g;
 // Matches a script end tag (case-insensitive) for XSS protection: either a
 // literal `</script>`, or a bare `</script` followed by one of the other
diff --git a/test/unit/method-bodies.js b/test/unit/method-bodies.js
new file mode 100644
index 0000000..1710a3e
--- /dev/null
+++ b/test/unit/method-bodies.js
@@ -0,0 +1,66 @@
+const { describe, it } = require('node:test');
+const { strictEqual } = require('node:assert');
+const serialize = require('../../');
+
+describe('method bodies containing other functions', function () {
+    it('round trips a method containing an arrow with destructured parameters', function () {
+        const input = {
+            method() {
+                const nested = ({ value }) => value;
+                return nested({ value: 42 });
+            }
+        };
+        const output = eval('(' + serialize(input) + ')');
+        strictEqual(output.method(), 42);
+    });
+
+    it('round trips a method containing a function declaration', function () {
+        const input = {
+            method() {
+                function nested() { return 42; }
+                return nested();
+            }
+        };
+        const output = eval('(' + serialize(input) + ')');
+        strictEqual(output.method(), 42);
+    });
+
+    it('preserves async methods containing arrows', async function () {
+        const input = {
+            async method() {
+                const nested = () => 42;
+                return nested();
+            }
+        };
+        const output = eval('(' + serialize(input) + ')');
+        strictEqual(await output.method(), 42);
+    });
+
+    it('preserves generator methods containing arrows', function () {
+        const input = {
+            *method() {
+                const nested = () => 42;
+                yield nested();
+            }
+        };
+        const output = eval('(' + serialize(input) + ')');
+        strictEqual(output.method().next().value, 42);
+    });
+});
+
+
+describe('outer function signatures', function () {
+    it('preserves async signatures with comments instead of spaces', async function () {
+        for (const fn of [async/**/function () { return 42; }, async/**/() => 42]) {
+            const output = eval('(' + serialize(fn) + ')');
+            strictEqual(await output(), 42);
+            strictEqual(output.constructor.name, 'AsyncFunction');
+        }
+    });
+
+    it('preserves arrows whose default arguments contain functions', function () {
+        const fn = (callback = function () { return 42; }) => callback();
+        const output = eval('(' + serialize(fn) + ')');
+        strictEqual(output(), 42);
+    });
+});