diff --git a/packages/base-styles/_z-index.scss b/packages/base-styles/_z-index.scss
index 95156a967d30cf..79be5af63a0d1f 100644
--- a/packages/base-styles/_z-index.scss
+++ b/packages/base-styles/_z-index.scss
@@ -30,6 +30,7 @@ $z-layers: (
 	".block-editor-url-input__suggestions": 30,
 	".edit-post-layout__footer": 30,
 	".interface-interface-skeleton__header": 30,
+	".edit-site-layout__header": 30,
 	".interface-interface-skeleton__content": 20,
 	".edit-widgets-header": 30,
 	".block-library-button__inline-link .block-editor-url-input__suggestions": 6, // URL suggestions for button block above sibling inserter
diff --git a/packages/block-editor/src/components/block-tools/use-block-toolbar-popover-props.js b/packages/block-editor/src/components/block-tools/use-block-toolbar-popover-props.js
index d218b1104139cf..b7212dbf790c64 100644
--- a/packages/block-editor/src/components/block-tools/use-block-toolbar-popover-props.js
+++ b/packages/block-editor/src/components/block-tools/use-block-toolbar-popover-props.js
@@ -11,28 +11,16 @@ import { useCallback, useLayoutEffect, useState } from '@wordpress/element';
 import { store as blockEditorStore } from '../../store';
 import { __unstableUseBlockElement as useBlockElement } from '../block-list/use-block-props/use-block-refs';
 
-const COMMON_PROPS = {
-	placement: 'top-start',
-};
+const TOOLBAR_MARGIN = 12;
 
-// By default the toolbar sets the `shift` prop. If the user scrolls the page
-// down the toolbar will stay on screen by adopting a sticky position at the
-// top of the viewport.
+// By default the toolbar sets the `shift` prop and flip properties.
+// If there is enough room, then once the block scrolls past the top of the screen,
+// then the toolbar is flipped to the bottom.
 const DEFAULT_PROPS = {
-	...COMMON_PROPS,
-	flip: false,
-	shift: true,
-};
-
-// When there isn't enough height between the top of the block and the editor
-// canvas, the `shift` prop is set to `false`, as it will cause the block to be
-// obscured. The `flip` behavior is enabled, which positions the toolbar below
-// the block. This only happens if the block is smaller than the viewport, as
-// otherwise the toolbar will be off-screen.
-const RESTRICTED_HEIGHT_PROPS = {
-	...COMMON_PROPS,
+	placement: 'top-start',
+	strategy: 'fixed',
 	flip: true,
-	shift: false,
+	shift: true,
 };
 
 /**
@@ -50,22 +38,27 @@ function getProps( contentElement, selectedBlockElement, toolbarHeight ) {
 	}
 
 	const blockRect = selectedBlockElement.getBoundingClientRect();
-	const contentRect = contentElement.getBoundingClientRect();
 
 	// The document element's clientHeight represents the viewport height.
 	const viewportHeight =
 		contentElement.ownerDocument.documentElement.clientHeight;
 
-	const hasSpaceForToolbarAbove =
-		blockRect.top - contentRect.top > toolbarHeight;
 	const isBlockTallerThanViewport =
 		blockRect.height > viewportHeight - toolbarHeight;
 
-	if ( hasSpaceForToolbarAbove || isBlockTallerThanViewport ) {
-		return DEFAULT_PROPS;
+	if ( isBlockTallerThanViewport ) {
+		return {
+			...DEFAULT_PROPS,
+			flip: false,
+			shift: { padding: toolbarHeight - TOOLBAR_MARGIN },
+		};
 	}
 
-	return RESTRICTED_HEIGHT_PROPS;
+	return {
+		...DEFAULT_PROPS,
+		flip: { padding: toolbarHeight },
+		shift: { padding: toolbarHeight - TOOLBAR_MARGIN },
+	};
 }
 
 /**
diff --git a/packages/components/CHANGELOG.md b/packages/components/CHANGELOG.md
index 833519075ccba7..a89c4afdbc7318 100644
--- a/packages/components/CHANGELOG.md
+++ b/packages/components/CHANGELOG.md
@@ -25,6 +25,7 @@
 -   `ResizableBox`: Prevent unnecessary paint on resize handles ([#46196](https://github.com/WordPress/gutenberg/pull/46196)).
 -   `Popover`: Prevent unnecessary paint caused by using outline ([#46201](https://github.com/WordPress/gutenberg/pull/46201)).
 -   `PaletteEdit`: Global styles: add onChange actions to color palette items [#45681](https://github.com/WordPress/gutenberg/pull/45681).
+-   `Popover`: Add support for padding in `flip` and `shift` props, add `strategy` prop ([#46085](https://github.com/WordPress/gutenberg/pull/46085)).
 
 ### Experimental
 
diff --git a/packages/components/src/popover/README.md b/packages/components/src/popover/README.md
index e012dce41e9a90..b18529595d94b8 100644
--- a/packages/components/src/popover/README.md
+++ b/packages/components/src/popover/README.md
@@ -125,7 +125,7 @@ Show the popover fullscreen on mobile viewports.
 
 -   Required: No
 
-### `flip`: `boolean`
+### `flip`: `FlipProps | boolean`
 
 Specifies whether the popover should flip across its axis if there isn't space for it in the normal placement.
 
@@ -133,6 +133,8 @@ When the using a 'top' placement, the popover will switch to a 'bottom' placemen
 
 The popover will retain its alignment of 'start' or 'end' when flipping.
 
+When passed an object, the amount of padding before flipping can be set using a `padding` property.
+
 -   Required: No
 -   Default: `true`
 
@@ -224,6 +226,22 @@ Adjusts the size of the popover to prevent its contents from going out of view w
 -   Required: No
 -   Default: `true`
 
+### `shift`: `ShiftProps | boolean`
+
+Enables the popover to shift in order to stay in view when meeting the viewport edges.
+
+When passed an object, the amount of padding before shifting can be set using a `padding` property.
+
+-   Required: No
+-   Default: `true`
+
+### `strategy`: `'absolute' | 'fixed'`
+
+Sets the type of CSS position property to use for the popover.
+
+-   Required: No
+-   Default: `'absolute'`
+
 ### `variant`: `'toolbar' | 'unstyled'`
 
 Specifies the popover's style.
diff --git a/packages/components/src/popover/index.tsx b/packages/components/src/popover/index.tsx
index 1d3b2af1dec1ae..e6906a51c1ecfd 100644
--- a/packages/components/src/popover/index.tsx
+++ b/packages/components/src/popover/index.tsx
@@ -181,6 +181,7 @@ const UnforwardedPopover = (
 		resize = true,
 		shift = false,
 		variant,
+		strategy: strategyProp = 'absolute',
 
 		// Deprecated props
 		__unstableForcePosition,
@@ -291,7 +292,14 @@ const UnforwardedPopover = (
 			},
 		},
 		offsetMiddleware( offsetProp ),
-		computedFlipProp ? flipMiddleware() : undefined,
+		computedFlipProp
+			? flipMiddleware( {
+					padding:
+						typeof computedFlipProp === 'object'
+							? computedFlipProp?.padding
+							: undefined,
+			  } )
+			: undefined,
 		computedResizeProp
 			? size( {
 					apply( sizeProps ) {
@@ -314,7 +322,7 @@ const UnforwardedPopover = (
 			? shiftMiddleware( {
 					crossAxis: true,
 					limiter: customLimitShift(),
-					padding: 1, // Necessary to avoid flickering at the edge of the viewport.
+					padding: typeof shift === 'object' ? shift?.padding : 1, // Necessary to avoid flickering at the edge of the viewport.
 			  } )
 			: undefined,
 		arrow( { element: arrowRef } ),
@@ -362,6 +370,7 @@ const UnforwardedPopover = (
 		middlewareData: { arrow: arrowData },
 	} = useFloating( {
 		placement: normalizedPlacementFromProps,
+		strategy: strategyProp,
 		middleware,
 		whileElementsMounted: ( referenceParam, floatingParam, updateParam ) =>
 			autoUpdate( referenceParam, floatingParam, updateParam, {
diff --git a/packages/components/src/popover/types.ts b/packages/components/src/popover/types.ts
index 96cb7e5fd6f863..6629fba50c92fa 100644
--- a/packages/components/src/popover/types.ts
+++ b/packages/components/src/popover/types.ts
@@ -26,6 +26,14 @@ export type VirtualElement = Pick< Element, 'getBoundingClientRect' > & {
 	ownerDocument?: Document;
 };
 
+export type FlipProps = {
+	padding?: number;
+};
+
+export type ShiftProps = {
+	padding?: number;
+};
+
 export type PopoverProps = {
 	/**
 	 * The name of the Slot in which the popover should be rendered. It should
@@ -67,7 +75,7 @@ export type PopoverProps = {
 	 *
 	 * @default true
 	 */
-	flip?: boolean;
+	flip?: FlipProps | boolean;
 	/**
 	 * By default, the _first tabbable element_ in the popover will receive focus
 	 * when it mounts. This is the same as setting this prop to `"firstElement"`.
@@ -133,7 +141,13 @@ export type PopoverProps = {
 	 *
 	 * @default false
 	 */
-	shift?: boolean;
+	shift?: ShiftProps | boolean;
+	/**
+	 * Sets the type of CSS position property to use.
+	 *
+	 * @default 'absolute'
+	 */
+	strategy?: 'absolute' | 'fixed';
 	/**
 	 * Specifies the popover's style.
 	 *
diff --git a/packages/edit-site/src/components/layout/style.scss b/packages/edit-site/src/components/layout/style.scss
index 81c7c9869f8d99..261fc5038be6d3 100644
--- a/packages/edit-site/src/components/layout/style.scss
+++ b/packages/edit-site/src/components/layout/style.scss
@@ -24,6 +24,7 @@
 	grid-area: header;
 	height: $header-height;
 	display: flex;
+	z-index: z-index(".edit-site-layout__header");
 }
 
 .edit-site-layout__logo {
diff --git a/packages/edit-widgets/src/components/header/style.scss b/packages/edit-widgets/src/components/header/style.scss
index 279182e48a624e..2af35e3940dfea 100644
--- a/packages/edit-widgets/src/components/header/style.scss
+++ b/packages/edit-widgets/src/components/header/style.scss
@@ -2,6 +2,7 @@
 	display: flex;
 	align-items: center;
 	justify-content: space-between;
+	background: $white;
 	height: $header-height;
 	padding: 0 $grid-unit-20;
 	overflow: auto;