diff --git a/src/draw/chrome.rs b/src/draw/chrome.rs
index d6f70be..3e03891 100644
--- a/src/draw/chrome.rs
+++ b/src/draw/chrome.rs
@@ -84,15 +84,23 @@ pub( crate ) fn apply_input_region(
 	wl_surface:   &WlSurface,
 	compositor:   &CompositorState,
 	input_region: Option<&[Rect]>,
+	scale:        u32,
 )
 {
 	if let Some( regions ) = input_region
 	{
 		if let Ok( region ) = Region::new( compositor )
 		{
+			// `Rect`s are physical (layout space); `wl_region` is logical.
+			let s = scale.max( 1 ) as f32;
 			for r in regions
 			{
-				region.add( r.x as i32, r.y as i32, r.width as i32, r.height as i32 );
+				region.add(
+					( r.x      / s ).round() as i32,
+					( r.y      / s ).round() as i32,
+					( r.width  / s ).round() as i32,
+					( r.height / s ).round() as i32,
+				);
 			}
 			wl_surface.set_input_region( Some( region.wl_region() ) );
 		}
diff --git a/src/draw/gles.rs b/src/draw/gles.rs
index 0938993..a5bb6dc 100644
--- a/src/draw/gles.rs
+++ b/src/draw/gles.rs
@@ -141,7 +141,7 @@ pub( crate ) fn draw_surface_full_gpu<Msg: Clone>(
 	ss.content_dirty   = false;
 
 	let wl_surface = ss.surface.wl_surface();
-	apply_input_region( wl_surface, compositor, input_region );
+	apply_input_region( wl_surface, compositor, input_region, scale );
 	// Frame callback request must precede the implicit commit done by
 	// `swap_buffers_with_damage`, so the compositor can attach it to this
 	// frame and not the previous one.
@@ -241,7 +241,7 @@ pub( crate ) fn draw_surface_partial_gpu<Msg: Clone>(
 	ss.content_dirty   = false;
 
 	let wl_surface = ss.surface.wl_surface();
-	apply_input_region( wl_surface, compositor, input_region );
+	apply_input_region( wl_surface, compositor, input_region, scale );
 	request_frame( wl_surface );
 	// Convert top-left dirty rects to EGL bottom-left coords for the
 	// swap-with-damage call.
diff --git a/src/draw/software.rs b/src/draw/software.rs
index 6ea9ee7..893b7b8 100644
--- a/src/draw/software.rs
+++ b/src/draw/software.rs
@@ -167,7 +167,7 @@ pub( crate ) fn draw_surface_full<Msg: Clone>(
 		}
 	}
 
-	apply_input_region( wl_surface, compositor, input_region );
+	apply_input_region( wl_surface, compositor, input_region, scale );
 	// Request a frame callback BEFORE commit so the compositor schedules it
 	// against this exact frame; sets `frame_pending` so the run loop won't
 	// try to draw this surface again until the callback fires.
@@ -282,7 +282,7 @@ pub( crate ) fn draw_surface_partial<Msg: Clone>(
 		wl_surface.damage_buffer( r.x as i32, r.y as i32, r.width as i32, r.height as i32 );
 	}
 
-	apply_input_region( wl_surface, compositor, input_region );
+	apply_input_region( wl_surface, compositor, input_region, scale );
 	request_frame( wl_surface );
 	wl_surface.commit();
 	ss.frame_pending = true;
diff --git a/src/event_loop/overlays_reconcile.rs b/src/event_loop/overlays_reconcile.rs
index 670c4c5..c5628da 100644
--- a/src/event_loop/overlays_reconcile.rs
+++ b/src/event_loop/overlays_reconcile.rs
@@ -99,7 +99,19 @@ pub( super ) fn reconcile_overlays<A: App>( data: &mut AppData<A> )
 		SurfaceKind::Window( ref w ) => Some( w.xdg_surface().clone() ),
 		_ => None,
 	};
-	let parent_scale = data.main.scale_factor.max( 1 ) as f32;
+	let parent_scale_i = data.main.scale_factor.max( 1 );
+	let parent_scale   = parent_scale_i as f32;
+	// `OverlaySpec::size` is physical pixels (the app's layout space); the
+	// layer-shell `set_size` is logical. They only coincide at scale 1, so
+	// convert here — without it a scale-2 overlay requests a surface twice
+	// its intended size. `0 = fill` survives the divide.
+	let to_logical_size = move | ( w, h ): ( u32, u32 ) | -> ( u32, u32 )
+	{
+		(
+			( w as f32 / parent_scale ).round() as u32,
+			( h as f32 / parent_scale ).round() as u32,
+		)
+	};
 	// Snapshot the previous-frame anchor lookup table so we can resolve
 	// `anchor_widget_id` → `Rect` without holding a borrow on `data.main`
 	// across the overlay-mut loop below.
@@ -122,7 +134,8 @@ pub( super ) fn reconcile_overlays<A: App>( data: &mut AppData<A> )
 			{
 				if let SurfaceKind::Layer( ref layer_surface ) = ss.surface
 				{
-					layer_surface.set_size( spec.size.0, spec.size.1 );
+					let ( lw, lh ) = to_logical_size( spec.size );
+					layer_surface.set_size( lw, lh );
 					layer_surface.commit();
 					ss.last_requested_size = spec.size;
 				}
@@ -272,7 +285,7 @@ pub( super ) fn reconcile_overlays<A: App>( data: &mut AppData<A> )
 			layer:              spec.layer.to_wlr_layer(),
 			exclusive_zone:     spec.exclusive_zone,
 			anchor:             spec.anchor,
-			size:               spec.size,
+			size:               to_logical_size( spec.size ),
 			keyboard_exclusive: spec.keyboard_exclusive,
 			namespace:          "ltk-overlay",
 		};
@@ -282,6 +295,11 @@ pub( super ) fn reconcile_overlays<A: App>( data: &mut AppData<A> )
 			surface.materialize( cs, layer_shell, qh, output );
 		}
 		let mut ss = SurfaceState::<A::Message>::new( surface, 0.0, String::new() );
+		// Inherit the parent's scale so the first configure allocates a
+		// HiDPI buffer and lays out at the right size from frame one,
+		// instead of rendering at scale 1 until `scale_factor_changed`
+		// lands a frame or two later.
+		ss.scale_factor        = parent_scale_i;
 		ss.last_requested_size = spec.size;
 		ss.layer_anchor        = Some( spec.anchor );
 		overlays_m.insert( spec.id, ss );