diff --git a/src/parser/plugins/types.ts b/src/parser/plugins/types.ts
index 27e20ecf..935c289a 100644
--- a/src/parser/plugins/types.ts
+++ b/src/parser/plugins/types.ts
@@ -12,9 +12,13 @@ import {tsParseTypeAnnotation} from "./typescript";
 // An apparent conditional expression could actually be an optional parameter in an arrow function.
 export function typedParseConditional(noIn: boolean): void {
   // If we see ?:, this can't possibly be a valid conditional. typedParseParenItem will be called
-  // later to finish off the arrow parameter.
-  if (match(tt.question) && lookaheadType() === tt.colon) {
-    return;
+  // later to finish off the arrow parameter. We also need to handle bare ? tokens for optional
+  // parameters without type annotations, i.e. ?, and ?) .
+  if (match(tt.question)) {
+    const nextType = lookaheadType();
+    if (nextType === tt.colon || nextType === tt.comma || nextType === tt.parenR) {
+      return;
+    }
   }
   baseParseConditional(noIn);
 }
diff --git a/test/types-test.ts b/test/types-test.ts
index 5991839f..7d2e1e2f 100644
--- a/test/types-test.ts
+++ b/test/types-test.ts
@@ -470,4 +470,21 @@ describe("type transforms", () => {
     `,
     );
   });
+
+  it("handles optional params without type annotations", () => {
+    assertTypeScriptAndFlowResult(
+      `
+      const test = (a?) => a;
+      function test2(a?) {
+        return a;
+      }
+    `,
+      `"use strict";
+      const test = (a) => a;
+      function test2(a) {
+        return a;
+      }
+    `,
+    );
+  });
 });