diff --git a/src/js/static-net-filtering.js b/src/js/static-net-filtering.js
index 85f05d7fc..ed1c74908 100644
--- a/src/js/static-net-filtering.js
+++ b/src/js/static-net-filtering.js
@@ -1777,12 +1777,18 @@ FilterParser.prototype.parse = function(raw) {
 
     // https://github.com/gorhill/uBlock/issues/1669#issuecomment-224822448
     // remove pointless leading *.
+    // https://github.com/gorhill/uBlock/issues/3034
+    // - We can remove anchoring if we need to match all at the start.
     if ( s.startsWith('*') ) {
         s = s.replace(/^\*+([^%0-9a-z])/, '$1');
+        this.anchor &= ~0x6;
     }
     // remove pointless trailing *
+    // https://github.com/gorhill/uBlock/issues/3034
+    // - We can remove anchoring if we need to match all at the end.
     if ( s.endsWith('*') ) {
         s = s.replace(/([^%0-9a-z])\*+$/, '$1');
+        this.anchor &= ~0x1;
     }
 
     // nothing left?