diff --git a/mwparserfromhell/parser/tokenizer.c b/mwparserfromhell/parser/tokenizer.c
index e0a2adb..aa1c00b 100644
--- a/mwparserfromhell/parser/tokenizer.c
+++ b/mwparserfromhell/parser/tokenizer.c
@@ -1037,17 +1037,12 @@ Tokenizer_is_free_link(Tokenizer* self, Py_UNICODE this, Py_UNICODE next)
     Py_UNICODE after = Tokenizer_READ(self, 2);
     int ctx = self->topstack->context;
 
-    return ((this == *"" || this == *"\n" || this == *"[" || this == *"]") ||
-            (this == *"|" && ctx & LC_TEMPLATE) ||
-            (this == *"=" && ctx & LC_TEMPLATE_PARAM_KEY) ||
-            (this == *"}" && next == *"}" && ctx & LC_TEMPLATE) ||
-            (this == *"}" && next == *"}" && after == *"}"
-                          && ctx & LC_ARGUMENT) ||
-            (this == *"=" && ctx & LC_HEADING) ||
-            (this == *"<" && next == *"/" && after != *"") ||
-            (this == *"<" && next != *"!" && !(ctx & LC_TAG_CLOSE)) ||
-            (this == *">" && ctx & LC_TAG_CLOSE) ||
-            (this == *"'" && next == *"'"));
+    return (this == *"" || this == *"\n" || this == *"[" || this == *"]" ||
+        this == *"<" || this == *">"  || (this == *"'" && next == *"'") ||
+        (this == *"|" && ctx & LC_TEMPLATE) ||
+        (this == *"=" && ctx & (LC_TEMPLATE_PARAM_KEY | LC_HEADING)) ||
+        (this == *"}" && next == *"}" &&
+            (ctx & LC_TEMPLATE || (after == *"}" && ctx & LC_ARGUMENT))));
 }
 
 /*
@@ -1073,7 +1068,19 @@ Tokenizer_really_parse_external_link(Tokenizer* self, int brackets,
     while (1) {
         this = Tokenizer_READ(self, 0);
         next = Tokenizer_READ(self, 1);
-        if (!brackets && Tokenizer_is_free_link(self, this, next)) {
+        if (this == *"&") {
+            PUSH_TAIL_BUFFER(*extra, NULL)
+            if (Tokenizer_parse_entity(self))
+                return NULL;
+        }
+        else if (this == *"<" && next == *"!"
+                 && Tokenizer_READ(self, 2) == *"-"
+                 && Tokenizer_READ(self, 3) == *"-") {
+            PUSH_TAIL_BUFFER(*extra, NULL)
+            if (Tokenizer_parse_comment(self))
+                return NULL;
+        }
+        else if (!brackets && Tokenizer_is_free_link(self, this, next)) {
             self->head--;
             return Tokenizer_pop(self);
         }
@@ -1086,18 +1093,6 @@ Tokenizer_really_parse_external_link(Tokenizer* self, int brackets,
         }
         else if (this == *"]")
             return Tokenizer_pop(self);
-        else if (this == *"&") {
-            PUSH_TAIL_BUFFER(*extra, NULL)
-            if (Tokenizer_parse_entity(self))
-                return NULL;
-        }
-        else if (this == *"<" && next == *"!"
-                 && Tokenizer_READ(self, 2) == *"-"
-                 && Tokenizer_READ(self, 3) == *"-") {
-            PUSH_TAIL_BUFFER(*extra, NULL)
-            if (Tokenizer_parse_comment(self))
-                return NULL;
-        }
         else if (this == *" ") {
             if (brackets) {
                 if (Tokenizer_emit(self, ExternalLinkSeparator))
diff --git a/mwparserfromhell/parser/tokenizer.py b/mwparserfromhell/parser/tokenizer.py
index bcc00ef..2c28718 100644
--- a/mwparserfromhell/parser/tokenizer.py
+++ b/mwparserfromhell/parser/tokenizer.py
@@ -389,16 +389,13 @@ class Tokenizer(object):
         """Return whether the current head is the end of a free link."""
         # Built from _parse()'s end sentinels:
         after, ctx = self._read(2), self._context
-        return (this is self.END or this in ("\n", "[", "]") or
-                this == "|" and ctx & contexts.TEMPLATE or
-                this == "=" and ctx & contexts.TEMPLATE_PARAM_KEY or
-                this == next == "}" and ctx & contexts.TEMPLATE or
-                this == next == after == "}" and ctx & contexts.ARGUMENT or
-                this == "=" and ctx & contexts.HEADING or
-                this == "<" and next == "/" and after is not self.END or
-                this == "<" and next != "!" and not ctx & contexts.TAG_CLOSE or
-                this == ">" and ctx & contexts.TAG_CLOSE or
-                this == next == "'")
+        equal_sign_contexts = contexts.TEMPLATE_PARAM_KEY | contexts.HEADING
+        return (this in (self.END, "\n", "[", "]", "<", ">") or
+                this == next == "'" or
+                (this == "|" and ctx & contexts.TEMPLATE) or
+                (this == "=" and ctx & equal_sign_contexts) or
+                (this == next == "}" and ctx & contexts.TEMPLATE) or
+                (this == next == after == "}" and ctx & contexts.ARGUMENT))
 
     def _really_parse_external_link(self, brackets):
         """Really parse an external link."""
@@ -414,18 +411,7 @@ class Tokenizer(object):
         tail = ""
         while True:
             this, next = self._read(), self._read(1)
-            if not brackets and self._is_free_link_end(this, next):
-                return self._pop(), tail, -1
-            elif this is self.END or this == "\n":
-                self._fail_route()
-            elif this == next == "{" and self._can_recurse():
-                if tail:
-                    self._emit_text(tail)
-                    tail = ""
-                self._parse_template_or_argument()
-            elif this == "]":
-                return self._pop(), tail, 0
-            elif this == "&":
+            if this == "&":
                 if tail:
                     self._emit_text(tail)
                     tail = ""
@@ -436,6 +422,17 @@ class Tokenizer(object):
                     self._emit_text(tail)
                     tail = ""
                 self._parse_comment()
+            elif not brackets and self._is_free_link_end(this, next):
+                return self._pop(), tail, -1
+            elif this is self.END or this == "\n":
+                self._fail_route()
+            elif this == next == "{" and self._can_recurse():
+                if tail:
+                    self._emit_text(tail)
+                    tail = ""
+                self._parse_template_or_argument()
+            elif this == "]":
+                return self._pop(), tail, 0
             elif " " in this:
                 before, after = this.split(" ", 1)
                 if brackets: