diff --git a/lib/inlines.js b/lib/inlines.js
index d2907b7a..fc870e13 100644
--- a/lib/inlines.js
+++ b/lib/inlines.js
@@ -577,7 +577,8 @@ var parseLinkDestination = function() {
                     this.pos += 1;
                     openparens -= 1;
                 }
-            } else if (reWhitespaceChar.exec(fromCodePoint(c)) !== null) {
+            } else if (c <= 0x20 || c === 0x7F) {
+                // ASCII space or control character (U+0000–1F, U+007F)
                 break;
             } else {
                 this.pos += 1;
diff --git a/test/test.js b/test/test.js
index 53d40270..94da0c55 100755
--- a/test/test.js
+++ b/test/test.js
@@ -181,6 +181,31 @@ var cases = [
         input: "abc\u0000xyz\u0000\n",
         expected: "<p>abc\ufffdxyz\ufffd</p>\n"
     },
+    {
+        name: "Issue #127 U+0001 in unbracketed link destination",
+        input: "[a](\x01)\n",
+        expected: "<p>[a](\x01)</p>\n"
+    },
+    {
+        name: "Issue #127 U+007F in unbracketed link destination",
+        input: "[a](\x7f)\n",
+        expected: "<p>[a](\x7f)</p>\n"
+    },
+    {
+        name: "Issue #127 control character inside unbracketed link destination",
+        input: "[a](foo\x07bar)\n",
+        expected: "<p>[a](foo\x07bar)</p>\n"
+    },
+    {
+        name: "Issue #127 U+0001 in unbracketed image destination",
+        input: "![a](\x01)\n",
+        expected: "<p>![a](\x01)</p>\n"
+    },
+    {
+        name: "Issue #127 control character in link reference destination",
+        input: "[foo]: /url\x01\n\n[foo]\n",
+        expected: "<p>[foo]: /url\x01</p>\n<p>[foo]</p>\n"
+    },
     {
         name: "alternate line endings",
         input: "- a\n- b\r- c\r\n- d",