diff --git a/packages/block-library/src/cover/edit.js b/packages/block-library/src/cover/edit.js
index 244390fd3a9ac..54833248a74d3 100644
--- a/packages/block-library/src/cover/edit.js
+++ b/packages/block-library/src/cover/edit.js
@@ -629,7 +629,7 @@ function CoverEdit( {
 		dimRatioToClass( dimRatio ),
 		{
 			'is-dark-theme': isDark,
-			'has-background-dim': dimRatio !== 0,
+			'has-background-dim': url && dimRatio !== 0,
 			'is-transient': isUploadingMedia,
 			'has-parallax': hasParallax,
 			'is-repeated': isRepeated,
@@ -639,6 +639,7 @@ function CoverEdit( {
 			'has-custom-content-position': ! isContentPositionCenter(
 				contentPosition
 			),
+			'is-default-background-color': ! overlayColor.class,
 		},
 		getPositionClassName( contentPosition )
 	);
diff --git a/packages/block-library/src/cover/save.js b/packages/block-library/src/cover/save.js
index 1b1de52e07521..1ddd572d9df16 100644
--- a/packages/block-library/src/cover/save.js
+++ b/packages/block-library/src/cover/save.js
@@ -76,7 +76,7 @@ export default function save( { attributes } ) {
 		dimRatioToClass( dimRatio ),
 		overlayColorClass,
 		{
-			'has-background-dim': dimRatio !== 0,
+			'has-background-dim': url && dimRatio !== 0,
 			'has-parallax': hasParallax,
 			'is-repeated': isRepeated,
 			'has-background-gradient': gradient || customGradient,
diff --git a/packages/block-library/src/cover/style.scss b/packages/block-library/src/cover/style.scss
index 43155f41d9ebf..bcdfbfcee5169 100644
--- a/packages/block-library/src/cover/style.scss
+++ b/packages/block-library/src/cover/style.scss
@@ -11,6 +11,7 @@
 	padding: 1em;
 	// This block has customizable padding, border-box makes that more predictable.
 	box-sizing: border-box;
+	color: $white;
 
 	&.has-parallax {
 		background-attachment: fixed;
@@ -33,17 +34,7 @@
 		background-size: auto;
 	}
 
-	/**
-	 * Set a default background color for has-background-dim _unless_ it includes another
-	 * background-color class (e.g. has-green-background-color). The presence of another
-	 * background-color class implies that another style will provide the background color
-	 * for the overlay.
-	 *
-	 * See:
-	 *   - Issue with background color specificity: https://github.com/WordPress/gutenberg/issues/26545
-	 *   - Issue with alternative fix: https://github.com/WordPress/gutenberg/issues/26545
-	 */
-	&.has-background-dim:not([class*="-background-color"]) {
+	&.is-default-background-color {
 		background-color: $black;
 	}
 
@@ -104,7 +95,6 @@
 	.wp-block-cover__inner-container {
 		width: 100%;
 		z-index: z-index(".wp-block-cover__inner-container");
-		color: $white;
 	}
 
 	p,