diff --git a/container.go b/container.go
index 9ea516b..728c988 100644
--- a/container.go
+++ b/container.go
@@ -368,15 +368,29 @@ func (c *Context) bringToFront(cnt *container) {
 }
 
 func (c *Context) hoveringRootContainer() *container {
-	p := c.pointingPosition()
+	return c.rootContainerAt(c.pointingPosition())
+}
+
+// rootContainerAt returns the topmost open root container whose hit area contains p, or nil if there is none.
+func (c *Context) rootContainerAt(p image.Point) *container {
 	for i := len(c.rootContainers) - 1; i >= 0; i-- {
 		cnt := c.rootContainers[i]
 		if !cnt.open {
 			continue
 		}
-		if p.In(cnt.layout.Bounds) {
+		if p.In(c.rootContainerHitBounds(cnt)) {
 			return cnt
 		}
 	}
 	return nil
 }
+
+// rootContainerHitBounds returns the area of a root container that receives pointing input.
+// A collapsed container shows only its title bar, so only the title bar receives input.
+func (c *Context) rootContainerHitBounds(cnt *container) image.Rectangle {
+	bounds := cnt.layout.Bounds
+	if cnt.collapsed {
+		bounds.Max.Y = min(bounds.Max.Y, bounds.Min.Y+c.style().titleHeight)
+	}
+	return bounds
+}
diff --git a/context.go b/context.go
index 2cfce8a..3e5eaa2 100644
--- a/context.go
+++ b/context.go
@@ -113,11 +113,7 @@ func (c *Context) update(f func(ctx *Context) error) (inputCapturingState InputC
 	// Check whether the cursor is on any of the root containers.
 	pt := c.pointingPosition()
 	for _, cnt := range c.rootContainers {
-		bounds := cnt.layout.Bounds
-		if cnt.collapsed {
-			bounds.Max.Y = cnt.layout.BodyBounds.Min.Y
-		}
-		if pt.In(bounds) {
+		if pt.In(c.rootContainerHitBounds(cnt)) {
 			inputCapturingState |= InputCapturingStateHover
 		}
 	}
diff --git a/debugui_test.go b/debugui_test.go
index 7bd8f9b..f1e28f2 100644
--- a/debugui_test.go
+++ b/debugui_test.go
@@ -138,3 +138,58 @@ func TestUnusedContainer(t *testing.T) {
 		t.Errorf("got: %v, want: %v", got, want)
 	}
 }
+
+func TestCollapsedWindowDoesNotCoverWindowsBelow(t *testing.T) {
+	const (
+		bottom = 0
+		top    = 1
+	)
+	var d debugui.DebugUI
+	update := func() {
+		t.Helper()
+		if _, err := d.Update(func(ctx *debugui.Context) error {
+			ctx.Window("Bottom", image.Rect(50, 70, 260, 180), func(layout debugui.ContainerLayout) {})
+			ctx.Window("Top", image.Rect(0, 0, 320, 240), func(layout debugui.ContainerLayout) {})
+			return nil
+		}); err != nil {
+			t.Fatal(err)
+		}
+	}
+	update()
+
+	// The title bar of Top is 24 pixels tall by default.
+	onTopTitleBar := image.Pt(10, 10)
+	onBottomBelowTopTitleBar := image.Pt(100, 100)
+	onTopBodyOnly := image.Pt(10, 200)
+	outside := image.Pt(400, 400)
+
+	testCases := []struct {
+		name  string
+		pt    image.Point
+		want  int
+		setup func()
+	}{
+		{name: "expanded title bar", pt: onTopTitleBar, want: top},
+		{name: "expanded body over bottom", pt: onBottomBelowTopTitleBar, want: top},
+		{name: "expanded body only", pt: onTopBodyOnly, want: top},
+		{name: "outside", pt: outside, want: -1},
+		{name: "collapsed title bar", pt: onTopTitleBar, want: top, setup: func() { d.SetRootContainerCollapsed(top, true) }},
+		{name: "collapsed title bar bottom edge", pt: image.Pt(10, 23), want: top},
+		{name: "collapsed just below title bar", pt: image.Pt(10, 24), want: -1},
+		{name: "collapsed body over bottom", pt: onBottomBelowTopTitleBar, want: bottom},
+		{name: "collapsed body only", pt: onTopBodyOnly, want: -1},
+		{name: "collapsed and moved, old title bar", pt: onTopTitleBar, want: -1, setup: func() { d.MoveRootContainer(top, image.Pt(0, 150)) }},
+		{name: "collapsed and moved, new title bar", pt: image.Pt(10, 160), want: top},
+		{name: "collapsed and moved, over bottom", pt: onBottomBelowTopTitleBar, want: bottom},
+		{name: "expanded again", pt: image.Pt(10, 200), want: top, setup: func() { d.SetRootContainerCollapsed(top, false) }},
+	}
+	for _, tc := range testCases {
+		if tc.setup != nil {
+			tc.setup()
+			update()
+		}
+		if got := d.RootContainerIndexAt(tc.pt); got != tc.want {
+			t.Errorf("%s: RootContainerIndexAt(%v): got: %d, want: %d", tc.name, tc.pt, got, tc.want)
+		}
+	}
+}
diff --git a/export_test.go b/export_test.go
index 280af4c..1e7784c 100644
--- a/export_test.go
+++ b/export_test.go
@@ -3,6 +3,8 @@
 
 package debugui
 
+import "image"
+
 func IDPartFromCaller() string {
 	pc := caller()
 	return idPartFromCaller(pc)
@@ -89,3 +91,23 @@ func TextIndexFromX(str string, x int) int {
 func TextWidth(str string) int {
 	return textWidth(str)
 }
+
+// RootContainerIndexAt returns the z-order index of the topmost root container hit at p, or -1.
+func (d *DebugUI) RootContainerIndexAt(p image.Point) int {
+	cnt := d.ctx.rootContainerAt(p)
+	for i, c := range d.ctx.rootContainers {
+		if c == cnt {
+			return i
+		}
+	}
+	return -1
+}
+
+func (d *DebugUI) SetRootContainerCollapsed(index int, collapsed bool) {
+	d.ctx.rootContainers[index].collapsed = collapsed
+}
+
+func (d *DebugUI) MoveRootContainer(index int, delta image.Point) {
+	cnt := d.ctx.rootContainers[index]
+	cnt.layout.Bounds = cnt.layout.Bounds.Add(delta)
+}