diff --git a/src/wp-admin/css/edit.css b/src/wp-admin/css/edit.css
index 7fa904ae1a..2033113664 100644
--- a/src/wp-admin/css/edit.css
+++ b/src/wp-admin/css/edit.css
@@ -725,6 +725,17 @@ form#tags-filter {
 	padding-left: 0;
 }
 
+/* Better position for the WordPress admin notices. */
+.privacy-settings .notice,
+.site-health .notice {
+	margin: 25px 20px 15px 22px;
+}
+
+.privacy-settings .notice ~ .notice,
+.site-health .notice ~ .notice {
+	margin-top: 5px;
+}
+
 /* Emulates .wrap h1 styling */
 .privacy-settings-header h1,
 .health-check-header h1 {
diff --git a/src/wp-admin/css/site-health.css b/src/wp-admin/css/site-health.css
index af8a43cc51..da65a93f3d 100644
--- a/src/wp-admin/css/site-health.css
+++ b/src/wp-admin/css/site-health.css
@@ -280,17 +280,6 @@ are styled in the Privacy section of edit.css */
 	padding-left: 20px;
 }
 
-
-/* Better position for the WordPress admin notices and update nag. */
-.site-health .notice {
-	margin: 5px 20px 15px 22px;
-}
-
-.site-health .update-nag {
-	margin-bottom: 20px;
-	margin-left: 22px;
-}
-
 .health-check-wp-paths-sizes.spinner {
 	visibility: visible;
 	float: none;