diff --git a/src/overlay.js b/src/overlay.js
index 61f5fa88..447e9c67 100644
--- a/src/overlay.js
+++ b/src/overlay.js
@@ -133,10 +133,11 @@
         this.elementWrapper.appendChild(this.element);
 
         if (this.element.id) {
-            this.elementWrapper.id = "overlay-wrapper-" + this.element.id;
-        } else {
-            this.elementWrapper.id = "overlay-wrapper";
+            this.elementWrapper.id = "overlay-wrapper-" + this.element.id; // Unique ID if element has one
         }
+        // Always add a class for styling & selection
+        this.elementWrapper.classList.add("openseadragon-overlay-wrapper");
+        
 
         this.style = this.elementWrapper.style;
         this._init(options);
@@ -498,4 +499,4 @@
         }
     };
 
-}(OpenSeadragon));
+}(OpenSeadragon));
\ No newline at end of file