diff --git a/addons/web_editor/static/src/scss/web_editor.frontend.scss b/addons/web_editor/static/src/scss/web_editor.frontend.scss
index 0b302c1b1c0..bc467ce0bbf 100644
--- a/addons/web_editor/static/src/scss/web_editor.frontend.scss
+++ b/addons/web_editor/static/src/scss/web_editor.frontend.scss
@@ -85,6 +85,17 @@
         > img[data-shape] {
             object-fit: contain !important;
         }
+
+        // Allowing "cover" for some hover effects.
+        &:not(.o_grid_item_image_contain) > img[data-shape$="geo_square"] {
+            &:not(
+                [data-hover-effect="dolly_zoom"],
+                [data-hover-effect="outline"],
+                [data-hover-effect="image_mirror_blur"],
+            ) {
+                object-fit: cover !important;
+            }
+        }
     }
 }
 
diff --git a/addons/website/static/src/js/editor/snippets.options.js b/addons/website/static/src/js/editor/snippets.options.js
index 521365d3ba1..5d2398729c8 100644
--- a/addons/website/static/src/js/editor/snippets.options.js
+++ b/addons/website/static/src/js/editor/snippets.options.js
@@ -4036,9 +4036,15 @@ options.registry.GridImage = options.Class.extend({
      * @override
      */
     _computeVisibility() {
+        // Special conditions for the hover effects.
+        const hasSquareShape = this.$target[0].dataset.shape === "web_editor/geometric/geo_square";
+        const effectAllowsOption = !["dolly_zoom", "outline", "image_mirror_blur"]
+            .includes(this.$target[0].dataset.hoverEffect);
+
         return this._super(...arguments)
             && !!this._getImageGridItem()
-            && !('shape' in this.$target[0].dataset);
+            && (!('shape' in this.$target[0].dataset)
+                || hasSquareShape && effectAllowsOption);
     },
     /**
      * @override