diff --git a/assets/stylesheets/_z-index.scss b/assets/stylesheets/_z-index.scss
index b21bff104a6ca7..b8f00482e84af7 100644
--- a/assets/stylesheets/_z-index.scss
+++ b/assets/stylesheets/_z-index.scss
@@ -5,7 +5,6 @@
 $z-layers: (
 	".editor-block-list__block-edit::before": 0,
 	".editor-block-switcher__arrow": 1,
-	".editor-block-list__block {core/image aligned left or right}": 20,
 	".editor-block-list__block {core/image aligned wide or fullwide}": 20,
 	".block-library-classic__toolbar": 10,
 	".editor-block-list__layout .reusable-block-indicator": 1,
@@ -48,9 +47,12 @@ $z-layers: (
 	".components-drop-zone": 100,
 	".components-drop-zone__content": 110,
 
-	// Block controls, particularly in nested contexts, floats aside block and
+	// The block mover, particularly in nested contexts,
 	// should overlap most block content.
-	".editor-block-list__block.is-{selected,hovered} .editor-block-{settings-menu,mover}": 80,
+	".editor-block-list__block.is-{selected,hovered} .editor-block-mover": 80,
+
+	// The block mover for floats should overlap the controls of adjacent blocks.
+	".editor-block-list__block {core/image aligned left or right}": 81,
 
 	// Small screen inner blocks overlay must be displayed above drop zone,
 	// settings menu, and movers.
diff --git a/packages/editor/src/components/block-list/block.js b/packages/editor/src/components/block-list/block.js
index 82e7154b76995b..fc795752580112 100644
--- a/packages/editor/src/components/block-list/block.js
+++ b/packages/editor/src/components/block-list/block.js
@@ -519,25 +519,25 @@ export class BlockListBlock extends Component {
 								clientId={ clientId }
 								rootClientId={ rootClientId }
 							/>
-							{ shouldRenderMovers && (
-								<BlockMover
-									clientIds={ clientId }
-									blockElementId={ blockElementId }
-									isFirst={ isFirst }
-									isLast={ isLast }
-									isHidden={ ! ( isHovered || isSelected ) || hoverArea !== 'left' }
-									isDraggable={
-										isDraggable !== false &&
-										( ! isPartOfMultiSelection && isMovable )
-									}
-									onDragStart={ this.onDragStart }
-									onDragEnd={ this.onDragEnd }
-								/>
-							) }
 							{ isFirstMultiSelected && (
 								<BlockMultiControls rootClientId={ rootClientId } />
 							) }
 							<div className="editor-block-list__block-edit">
+								{ shouldRenderMovers && (
+									<BlockMover
+										clientIds={ clientId }
+										blockElementId={ blockElementId }
+										isFirst={ isFirst }
+										isLast={ isLast }
+										isHidden={ ! ( isHovered || isSelected ) || hoverArea !== 'left' }
+										isDraggable={
+											isDraggable !== false &&
+											( ! isPartOfMultiSelection && isMovable )
+										}
+										onDragStart={ this.onDragStart }
+										onDragEnd={ this.onDragEnd }
+									/>
+								) }
 								{ shouldShowBreadcrumb && (
 									<BlockBreadcrumb
 										clientId={ clientId }
diff --git a/packages/editor/src/components/block-list/style.scss b/packages/editor/src/components/block-list/style.scss
index b89d2ac389494a..a024bb2198d062 100644
--- a/packages/editor/src/components/block-list/style.scss
+++ b/packages/editor/src/components/block-list/style.scss
@@ -1,8 +1,8 @@
 .editor-block-list__layout .components-draggable__clone {
-	// Hide the Block UI when dragging the block
-	// This ensures the page scroll properly (no sticky elements)
+	// Hide the Block UI when dragging the block.
+	// This ensures the page scroll properly (no sticky elements).
 	.editor-block-contextual-toolbar {
-		// I think important is fine here to avoid over complexing the selector
+		// It's probably okay to use !important here to avoid over-complicating the selector.
 		display: none !important;
 	}
 }
@@ -127,7 +127,7 @@
 		}
 	}
 
-	// Selected style
+	// Selected style.
 	&.is-selected > .editor-block-list__block-edit::before {
 		// Use opacity to work in various editor styles.
 		outline: $border-width solid $dark-opacity-light-500;
@@ -137,12 +137,12 @@
 		}
 	}
 
-	// Hover style
+	// Hover style.
 	&.is-hovered > .editor-block-list__block-edit::before {
 		outline: $border-width solid theme(outlines);
 	}
 
-	// Spotlight mode
+	// Spotlight mode.
 	&.is-focus-mode:not(.is-multi-selected) {
 		opacity: 0.5;
 		transition: opacity 0.1s linear;
@@ -168,7 +168,7 @@
 		background-color: $blue-medium-highlight;
 	}
 
-	// selection style for multiple blocks
+	// Selection style for multiple blocks.
 	&.is-multi-selected *::selection {
 		background-color: transparent;
 	}
@@ -179,7 +179,7 @@
 		// Use opacity to work in various editor styles.
 		mix-blend-mode: multiply;
 
-		// Collapse extra vertical padding on selection
+		// Collapse extra vertical padding on selection.
 		top: -$block-padding;
 		bottom: -$block-padding;
 
@@ -293,12 +293,6 @@
 			margin-bottom: $border-width;
 		}
 
-		// Hide all additional UI on floats.
-		.editor-block-mover,
-		.editor-block-list__block-mobile-toolbar {
-			display: none;
-		}
-
 		// Position toolbar better on mobile.
 		.editor-block-contextual-toolbar {
 			width: auto;
@@ -506,7 +500,8 @@
 .editor-block-list__block {
 
 	// Left and right block settings and mover.
-	> .editor-block-mover {
+	&.is-multi-selected > .editor-block-mover,
+	> .editor-block-list__block-edit > .editor-block-mover {
 		position: absolute;
 		width: $block-side-ui-width + $block-side-ui-clearance;
 
@@ -516,7 +511,8 @@
 	}
 
 	// Position depending on whether selected or not.
-	> .editor-block-mover {
+	&.is-multi-selected > .editor-block-mover,
+	> .editor-block-list__block-edit > .editor-block-mover {
 		top: -$block-padding - $border-width;
 	}
 
@@ -526,24 +522,60 @@
 		&.is-selected,
 		&.is-hovered {
 			.editor-block-mover {
-				z-index: z-index(".editor-block-list__block.is-{selected,hovered} .editor-block-{settings-menu,mover}");
+				z-index: z-index(".editor-block-list__block.is-{selected,hovered} .editor-block-mover");
 			}
 		}
 	}
 
 	// Left side UI.
-	> .editor-block-mover {
+	&.is-multi-selected > .editor-block-mover,
+	> .editor-block-list__block-edit > .editor-block-mover {
 		padding-right: $block-side-ui-clearance;
 
-		// Position for top level blocks
-		left: -$block-side-ui-width - $block-side-ui-clearance;
+		// Position for top level blocks.
+		left: -$block-side-ui-width - $block-side-ui-clearance - $block-padding - $border-width;
 
-		// Mobile
+		// Hide on mobile, as mobile has a separate solution.
 		display: none;
 		@include break-small() {
 			display: block;
 		}
 	}
+
+	&.is-multi-selected > .editor-block-mover {
+		left: -$block-side-ui-width - $block-side-ui-clearance;
+	}
+
+	// For floats, show block mover when block is selected, and never on hover.
+	&[data-align="left"],
+	&[data-align="right"] {
+		// Show always when the block is selected.
+		&.is-selected > .editor-block-list__block-edit > .editor-block-mover {
+			// Don't show on mobile, allow the special mobile toolbar to work there.
+			display: none;
+			@include break-small() {
+				display: block;
+				opacity: 1;
+				animation: none;
+
+				// Make wider and taller to make "safe" hover area bigger.
+				// The intent is to make it less likely that you hover float-adjacent
+				// blocks that visually appear below the block.
+				width: $block-side-ui-width + $block-side-ui-clearance + $block-padding + $border-width;
+				height: auto;
+				padding-bottom: $block-padding;
+
+				// Unset the negative top margin, or it might overlap the block toolbar.
+				margin-top: 0;
+			}
+		}
+
+		// Don't show on hover, or on the "ghost" when dragging.
+		&.is-hovered > .editor-block-list__block-edit > .editor-block-mover,
+		&.is-dragging > .editor-block-list__block-edit > .editor-block-mover {
+			display: none;
+		}
+	}
 }
 
 
diff --git a/packages/editor/src/components/block-mover/style.scss b/packages/editor/src/components/block-mover/style.scss
index 8c6a0b6e4136cb..12ebccbe0035e4 100644
--- a/packages/editor/src/components/block-mover/style.scss
+++ b/packages/editor/src/components/block-mover/style.scss
@@ -87,6 +87,8 @@
 .editor-block-mover__control-drag-handle:not(:disabled):not([aria-disabled="true"]):not(.is-default),
 .editor-block-mover__control {
 	@include break-small() {
+		.editor-block-list__layout [data-align="right"] &,
+		.editor-block-list__layout [data-align="left"] &,
 		.editor-block-list__layout .editor-block-list__layout & {
 			background: $white;
 			box-shadow: inset 0 0 0 1px $light-gray-500;