diff --git a/packages/base-styles/_z-index.scss b/packages/base-styles/_z-index.scss
index fdf3ee586a9c3..945755f512ae7 100644
--- a/packages/base-styles/_z-index.scss
+++ b/packages/base-styles/_z-index.scss
@@ -140,6 +140,7 @@ $z-layers: (
 	".components-popover.block-editor-inserter__popover": 99999,
 	".components-popover.table-of-contents__popover": 99998,
 	".components-popover.interface-more-menu__content": 99998,
+	".components-popover.more-menu__content": 99998,
 	".components-popover.block-editor-rich-text__inline-format-toolbar": 99998,
 	".components-popover.block-editor-warning__dropdown": 99998,
 
diff --git a/packages/customize-widgets/src/components/more-menu/index.js b/packages/customize-widgets/src/components/more-menu/index.js
index 9a276976dc1fd..a0fb374057ec3 100644
--- a/packages/customize-widgets/src/components/more-menu/index.js
+++ b/packages/customize-widgets/src/components/more-menu/index.js
@@ -9,10 +9,9 @@ import {
 } from '@wordpress/components';
 import { useState } from '@wordpress/element';
 import { __, _x } from '@wordpress/i18n';
-import { external } from '@wordpress/icons';
+import { external, moreVertical } from '@wordpress/icons';
 import { displayShortcut } from '@wordpress/keycodes';
 import { useShortcut } from '@wordpress/keyboard-shortcuts';
-import { MoreMenuDropdown } from '@wordpress/interface';
 import { PreferenceToggleMenuItem } from '@wordpress/preferences';
 
 /**
@@ -35,7 +34,18 @@ export default function MoreMenu() {
 
 	return (
 		<>
-			<MoreMenuDropdown as={ ToolbarDropdownMenu }>
+			<ToolbarDropdownMenu
+				icon={ moreVertical }
+				label={ __( 'Options' ) }
+				popoverProps={ {
+					placement: 'bottom-end',
+					className: 'more-menu-dropdown__content',
+				} }
+				toggleProps={ {
+					tooltipPosition: 'bottom',
+					size: 'compact',
+				} }
+			>
 				{ () => (
 					<>
 						<MenuGroup label={ _x( 'View', 'noun' ) }>
@@ -106,7 +116,7 @@ export default function MoreMenu() {
 						</MenuGroup>
 					</>
 				) }
-			</MoreMenuDropdown>
+			</ToolbarDropdownMenu>
 			<KeyboardShortcutHelpModal
 				isModalActive={ isKeyboardShortcutsModalActive }
 				toggleModal={ toggleKeyboardShortcutsModal }
diff --git a/packages/customize-widgets/src/components/more-menu/style.scss b/packages/customize-widgets/src/components/more-menu/style.scss
new file mode 100644
index 0000000000000..e618ba729c1ab
--- /dev/null
+++ b/packages/customize-widgets/src/components/more-menu/style.scss
@@ -0,0 +1,3 @@
+.components-popover.more-menu-dropdown__content {
+	z-index: z-index(".components-popover.more-menu__content");
+}
diff --git a/packages/customize-widgets/src/style.scss b/packages/customize-widgets/src/style.scss
index c3679470e5c98..9596237895953 100644
--- a/packages/customize-widgets/src/style.scss
+++ b/packages/customize-widgets/src/style.scss
@@ -2,6 +2,7 @@
 @import "./components/header/style.scss";
 @import "./components/inserter/style.scss";
 @import "./components/keyboard-shortcut-help-modal/style.scss";
+@import "./components/more-menu/style.scss";
 @import "./components/sidebar-block-editor/style.scss";
 @import "./components/welcome-guide/style.scss";
 @import "./controls/style.scss";
diff --git a/packages/edit-post/src/components/header/more-menu/index.js b/packages/edit-post/src/components/header/more-menu/index.js
index 9ed41def2d80f..0924af9ecaf74 100644
--- a/packages/edit-post/src/components/header/more-menu/index.js
+++ b/packages/edit-post/src/components/header/more-menu/index.js
@@ -2,14 +2,11 @@
  * WordPress dependencies
  */
 import { __ } from '@wordpress/i18n';
-import { MenuGroup } from '@wordpress/components';
-import {
-	ActionItem,
-	MoreMenuDropdown,
-	PinnedItems,
-} from '@wordpress/interface';
+import { MenuGroup, DropdownMenu } from '@wordpress/components';
+import { ActionItem, PinnedItems } from '@wordpress/interface';
 import { useViewportMatch } from '@wordpress/compose';
 import { privateApis as editorPrivateApis } from '@wordpress/editor';
+import { moreVertical } from '@wordpress/icons';
 
 /**
  * Internal dependencies
@@ -25,10 +22,17 @@ const MoreMenu = ( { showIconLabels } ) => {
 	const isLargeViewport = useViewportMatch( 'large' );
 
 	return (
-		<MoreMenuDropdown
+		<DropdownMenu
+			icon={ moreVertical }
+			label={ __( 'Options' ) }
+			popoverProps={ {
+				placement: 'bottom-end',
+				className: 'more-menu-dropdown__content',
+			} }
 			toggleProps={ {
-				showTooltip: ! showIconLabels,
 				...( showIconLabels && { variant: 'tertiary' } ),
+				tooltipPosition: 'bottom',
+				showTooltip: ! showIconLabels,
 				size: 'compact',
 			} }
 		>
@@ -54,7 +58,7 @@ const MoreMenu = ( { showIconLabels } ) => {
 					</MenuGroup>
 				</>
 			) }
-		</MoreMenuDropdown>
+		</DropdownMenu>
 	);
 };
 
diff --git a/packages/edit-post/src/components/header/style.scss b/packages/edit-post/src/components/header/style.scss
index 8bea8a7993b8d..5dfec8eabe339 100644
--- a/packages/edit-post/src/components/header/style.scss
+++ b/packages/edit-post/src/components/header/style.scss
@@ -322,3 +322,7 @@
 		z-index: 35;
 	}
 }
+
+.components-popover.more-menu-dropdown__content {
+	z-index: z-index(".components-popover.more-menu__content");
+}
diff --git a/packages/edit-site/src/components/header-edit-mode/more-menu/index.js b/packages/edit-site/src/components/header-edit-mode/more-menu/index.js
index ef8e7ee0c40f8..00a61aa7492ec 100644
--- a/packages/edit-site/src/components/header-edit-mode/more-menu/index.js
+++ b/packages/edit-site/src/components/header-edit-mode/more-menu/index.js
@@ -4,13 +4,14 @@
 import { __, _x } from '@wordpress/i18n';
 import { useSelect, useDispatch } from '@wordpress/data';
 import { displayShortcut } from '@wordpress/keycodes';
-import { external } from '@wordpress/icons';
-import { MenuGroup, MenuItem, VisuallyHidden } from '@wordpress/components';
+import { external, moreVertical } from '@wordpress/icons';
 import {
-	ActionItem,
-	MoreMenuDropdown,
-	store as interfaceStore,
-} from '@wordpress/interface';
+	MenuGroup,
+	MenuItem,
+	VisuallyHidden,
+	DropdownMenu,
+} from '@wordpress/components';
+import { ActionItem, store as interfaceStore } from '@wordpress/interface';
 import {
 	PreferenceToggleMenuItem,
 	store as preferencesStore,
@@ -55,10 +56,18 @@ export default function MoreMenu( { showIconLabels } ) {
 
 	return (
 		<>
-			<MoreMenuDropdown
+			<DropdownMenu
+				icon={ moreVertical }
+				label={ __( 'Options' ) }
+				popoverProps={ {
+					placement: 'bottom-end',
+					className: 'more-menu-dropdown__content',
+				} }
 				toggleProps={ {
 					showTooltip: ! showIconLabels,
 					...( showIconLabels && { variant: 'tertiary' } ),
+					tooltipPosition: 'bottom',
+					size: 'compact',
 				} }
 			>
 				{ ( { onClose } ) => (
@@ -162,7 +171,7 @@ export default function MoreMenu( { showIconLabels } ) {
 						</MenuGroup>
 					</>
 				) }
-			</MoreMenuDropdown>
+			</DropdownMenu>
 			<KeyboardShortcutHelpModal />
 			<EditSitePreferencesModal />
 		</>
diff --git a/packages/edit-site/src/components/header-edit-mode/style.scss b/packages/edit-site/src/components/header-edit-mode/style.scss
index e47c51d94c434..b87da10d6db6e 100644
--- a/packages/edit-site/src/components/header-edit-mode/style.scss
+++ b/packages/edit-site/src/components/header-edit-mode/style.scss
@@ -256,3 +256,7 @@ $header-toolbar-min-width: 335px;
 .edit-site-header-edit-mode__block-tools-toggle {
 	margin-left: 2px; // Allow focus ring to be fully visible
 }
+
+.components-popover.more-menu-dropdown__content {
+	z-index: z-index(".components-popover.more-menu__content");
+}
diff --git a/packages/edit-widgets/src/components/more-menu/index.js b/packages/edit-widgets/src/components/more-menu/index.js
index bb3e01bd19e26..2613f3d605ff8 100644
--- a/packages/edit-widgets/src/components/more-menu/index.js
+++ b/packages/edit-widgets/src/components/more-menu/index.js
@@ -1,11 +1,15 @@
 /**
  * WordPress dependencies
  */
-import { MenuGroup, MenuItem, VisuallyHidden } from '@wordpress/components';
+import {
+	MenuGroup,
+	MenuItem,
+	VisuallyHidden,
+	DropdownMenu,
+} from '@wordpress/components';
 import { useState } from '@wordpress/element';
 import { __, _x } from '@wordpress/i18n';
-import { external } from '@wordpress/icons';
-import { MoreMenuDropdown } from '@wordpress/interface';
+import { external, moreVertical } from '@wordpress/icons';
 import { PreferenceToggleMenuItem } from '@wordpress/preferences';
 import { displayShortcut } from '@wordpress/keycodes';
 import { useShortcut } from '@wordpress/keyboard-shortcuts';
@@ -34,7 +38,18 @@ export default function MoreMenu() {
 
 	return (
 		<>
-			<MoreMenuDropdown>
+			<DropdownMenu
+				icon={ moreVertical }
+				label={ __( 'Options' ) }
+				popoverProps={ {
+					placement: 'bottom-end',
+					className: 'more-menu-dropdown__content',
+				} }
+				toggleProps={ {
+					tooltipPosition: 'bottom',
+					size: 'compact',
+				} }
+			>
 				{ ( onClose ) => (
 					<>
 						{ isLargeViewport && (
@@ -134,7 +149,7 @@ export default function MoreMenu() {
 						</MenuGroup>
 					</>
 				) }
-			</MoreMenuDropdown>
+			</DropdownMenu>
 			<KeyboardShortcutHelpModal
 				isModalActive={ isKeyboardShortcutsModalActive }
 				toggleModal={ toggleKeyboardShortcutsModal }
diff --git a/packages/edit-widgets/src/components/more-menu/style.scss b/packages/edit-widgets/src/components/more-menu/style.scss
new file mode 100644
index 0000000000000..e618ba729c1ab
--- /dev/null
+++ b/packages/edit-widgets/src/components/more-menu/style.scss
@@ -0,0 +1,3 @@
+.components-popover.more-menu-dropdown__content {
+	z-index: z-index(".components-popover.more-menu__content");
+}
diff --git a/packages/edit-widgets/src/style.scss b/packages/edit-widgets/src/style.scss
index ef92cd914a4fc..62a6f63cd4850 100644
--- a/packages/edit-widgets/src/style.scss
+++ b/packages/edit-widgets/src/style.scss
@@ -7,6 +7,7 @@
 @import "./components/sidebar/style.scss";
 @import "./components/notices/style.scss";
 @import "./components/layout/style.scss";
+@import "./components/more-menu/style.scss";
 @import "./components/welcome-guide/style.scss";
 @import "./components/widget-areas-block-editor-content/style.scss";
 @import "./components/secondary-sidebar/style.scss";
diff --git a/packages/interface/src/components/index.js b/packages/interface/src/components/index.js
index 1f0cb9e8bbdbe..a96d3304db7c5 100644
--- a/packages/interface/src/components/index.js
+++ b/packages/interface/src/components/index.js
@@ -3,6 +3,5 @@ export { default as ComplementaryAreaMoreMenuItem } from './complementary-area-m
 export { default as FullscreenMode } from './fullscreen-mode';
 export { default as InterfaceSkeleton } from './interface-skeleton';
 export { default as PinnedItems } from './pinned-items';
-export { default as MoreMenuDropdown } from './more-menu-dropdown';
 export { default as ActionItem } from './action-item';
 export { default as NavigableRegion } from './navigable-region';
diff --git a/packages/interface/src/components/more-menu-dropdown/README.md b/packages/interface/src/components/more-menu-dropdown/README.md
deleted file mode 100644
index 15ea2510595b3..0000000000000
--- a/packages/interface/src/components/more-menu-dropdown/README.md
+++ /dev/null
@@ -1,74 +0,0 @@
-# MoreMenuDropdown
-
-`MoreMenuDropdown` is a convenient component for rendering an editor 'more' menu. This is typically a menu that provides:
-
-- menu items for quick toggling editor preferences.
-- a way to open dialogs for keyboard shortcuts and editor preferences.
-- links to help.
-
-This component implements a `DropdownMenu` component from the `@wordpress/components` package.
-
-Note that just like the `DropdownMenu` component, this component accepts a render callback, which child elements should be returned from.
-
-## Example
-
-```jsx
-function MyEditorMenu() {
-	return (
-		<MoreMenuDropdown>
-			{ () => (
-				<MenuGroup label={ __( 'Features' ) }>
-					<MenuItem>
-						{ __( 'Keyboard Shortcuts' ) }
-					</MenuItem>
-					<MenuItem>
-						{ __( 'Editor Preferences' ) }
-					</MenuItem>
-				</MenuGroup>
-			) }
-		</MoreMenuDropdown>
-	);
-}
-```
-
-## Props
-
-### as
-
-Provide a component that the dropdown should render as. This may be useful if you need `MoreMenuDropdown` to render a `ToolbarDropdownMenu` instead of a `DropdownMenu`. Defaults to `DropdownMenu`.
-
--   Type: `Component`
--   Required: No.
-
-### className
-
-Provide an additional class name to the dropdown component.
-
--   Type: `String`
--   Required: No
-
-### label
-
-Change the label of the button that opens the dropdown.
-
--   Default: 'Options'
--   Type: `String`
--   Required: No
-
-### popoverProps
-
-Override or extend the dropdown's popover props.
-
-See the documentation for the `DropdownMenu` and `Popover` components in the `@wordpress/components` package for more information.
-
--   Type: `Object`
--   Required: No
-
-### toggleProps
-
-Override or extend the dropdown's toggle props.
-
-See the documentation for the `DropdownMenu` and `Button` components in the `@wordpress/components` package for more information.
-
--   Type: `Object`
--   Required: No
diff --git a/packages/interface/src/components/more-menu-dropdown/index.js b/packages/interface/src/components/more-menu-dropdown/index.js
deleted file mode 100644
index dafa4b2e4b3b4..0000000000000
--- a/packages/interface/src/components/more-menu-dropdown/index.js
+++ /dev/null
@@ -1,47 +0,0 @@
-/**
- * External dependencies
- */
-import classnames from 'classnames';
-
-/**
- * WordPress dependencies
- */
-import { DropdownMenu } from '@wordpress/components';
-import { __ } from '@wordpress/i18n';
-import { moreVertical } from '@wordpress/icons';
-
-export default function MoreMenuDropdown( {
-	as: DropdownComponent = DropdownMenu,
-	className,
-	/* translators: button label text should, if possible, be under 16 characters. */
-	label = __( 'Options' ),
-	popoverProps,
-	toggleProps,
-	children,
-} ) {
-	return (
-		<DropdownComponent
-			className={ classnames(
-				'interface-more-menu-dropdown',
-				className
-			) }
-			icon={ moreVertical }
-			label={ label }
-			popoverProps={ {
-				placement: 'bottom-end',
-				...popoverProps,
-				className: classnames(
-					'interface-more-menu-dropdown__content',
-					popoverProps?.className
-				),
-			} }
-			toggleProps={ {
-				tooltipPosition: 'bottom',
-				...toggleProps,
-				size: 'compact',
-			} }
-		>
-			{ ( onClose ) => children( onClose ) }
-		</DropdownComponent>
-	);
-}
diff --git a/packages/interface/src/components/more-menu-dropdown/style.scss b/packages/interface/src/components/more-menu-dropdown/style.scss
deleted file mode 100644
index a2b9b1481677e..0000000000000
--- a/packages/interface/src/components/more-menu-dropdown/style.scss
+++ /dev/null
@@ -1,34 +0,0 @@
-.interface-more-menu-dropdown {
-	margin-left: -4px;
-
-	// the padding and margin of the more menu is intentionally non-standard
-	.components-button {
-		width: auto;
-		padding: 0 2px;
-	}
-
-	@include break-small() {
-		margin-left: 0;
-
-		.components-button {
-			padding: 0 4px;
-		}
-	}
-}
-
-.interface-more-menu-dropdown__content .components-popover__content {
-	min-width: 300px;
-
-	// Let the menu scale to fit items.
-	@include break-mobile() {
-		max-width: $break-mobile;
-	}
-
-	.components-dropdown-menu__menu {
-		padding: 0;
-	}
-}
-
-.components-popover.interface-more-menu-dropdown__content {
-	z-index: z-index(".components-popover.interface-more-menu__content");
-}
diff --git a/packages/interface/src/style.scss b/packages/interface/src/style.scss
index e6950de411156..d7f1e35e6e661 100644
--- a/packages/interface/src/style.scss
+++ b/packages/interface/src/style.scss
@@ -2,5 +2,4 @@
 @import "./components/complementary-area/style.scss";
 @import "./components/fullscreen-mode/style.scss";
 @import "./components/interface-skeleton/style.scss";
-@import "./components/more-menu-dropdown/style.scss";
 @import "./components/pinned-items/style.scss";
diff --git a/packages/preferences/README.md b/packages/preferences/README.md
index f35f4cdc4e9b9..448eb69a9b363 100644
--- a/packages/preferences/README.md
+++ b/packages/preferences/README.md
@@ -138,12 +138,10 @@ wp.data.dispatch( 'core/preferences' ).setPersistenceLayer( {
 
 The `PreferenceToggleMenuItem` components can be used with a `DropdownMenu` to implement a menu for changing preferences.
 
-Also see the `MoreMenuDropdown` component from the `@wordpress/interface` package for implementing a more menu.
-
 ```jsx
 function MyEditorMenu() {
 	return (
-		<MoreMenuDropdown>
+		<DropdownMenu>
 			{ () => (
 				<MenuGroup label={ __( 'Features' ) }>
 					<PreferenceToggleMenuItem
@@ -156,7 +154,7 @@ function MyEditorMenu() {
 					/>
 				</MenuGroup>
 			) }
-		</MoreMenuDropdown>
+		</DropdownMenu>
 	);
 }
 ```