diff --git a/ezgui/src/canvas.rs b/ezgui/src/canvas.rs
index 58dcce4a76..6ad283f49d 100644
--- a/ezgui/src/canvas.rs
+++ b/ezgui/src/canvas.rs
@@ -30,7 +30,6 @@ pub struct Canvas {
 
     // TODO Bit weird and hacky to mutate inside of draw() calls.
     pub(crate) covered_areas: RefCell<Vec<ScreenRectangle>>,
-    pub(crate) covered_polygons: RefCell<Vec<Polygon>>,
 
     // Kind of just ezgui state awkwardly stuck here...
     pub(crate) lctrl_held: bool,
@@ -63,7 +62,6 @@ impl Canvas {
             map_dims: (0.0, 0.0),
 
             covered_areas: RefCell::new(Vec::new()),
-            covered_polygons: RefCell::new(Vec::new()),
 
             lctrl_held: false,
             button_tooltip: None,
@@ -127,10 +125,9 @@ impl Canvas {
 
     pub(crate) fn start_drawing(&self) {
         self.covered_areas.borrow_mut().clear();
-        self.covered_polygons.borrow_mut().clear();
     }
 
-    pub fn mark_covered_area(&self, rect: ScreenRectangle) {
+    pub(crate) fn mark_covered_area(&self, rect: ScreenRectangle) {
         self.covered_areas.borrow_mut().push(rect);
     }
 
@@ -147,11 +144,6 @@ impl Canvas {
                     return None;
                 }
             }
-            for c in self.covered_polygons.borrow().iter() {
-                if c.contains_pt(pt.to_pt()) {
-                    return None;
-                }
-            }
 
             Some(self.screen_to_map(pt))
         } else {
diff --git a/ezgui/src/drawing.rs b/ezgui/src/drawing.rs
index 7ffa5088c0..bf0466e803 100644
--- a/ezgui/src/drawing.rs
+++ b/ezgui/src/drawing.rs
@@ -242,6 +242,12 @@ impl<'a> GfxCtx<'a> {
             .mark_covered_area(text::draw_text_bubble(self, top_left, txt, dims, true));
     }
 
+    pub(crate) fn draw_blocking_text_at_screenspace_topleft(&mut self, txt: &Text, pt: ScreenPt) {
+        let dims = self.text_dims(&txt);
+        self.canvas
+            .mark_covered_area(text::draw_text_bubble(self, pt, txt, dims, true));
+    }
+
     pub fn get_screen_bounds(&self) -> Bounds {
         self.canvas.get_screen_bounds()
     }
@@ -272,12 +278,6 @@ impl<'a> GfxCtx<'a> {
         );
     }
 
-    pub fn draw_text_at_screenspace_topleft(&mut self, txt: &Text, pt: ScreenPt) {
-        let dims = self.text_dims(&txt);
-        self.canvas
-            .mark_covered_area(text::draw_text_bubble(self, pt, txt, dims, true));
-    }
-
     pub fn draw_mouse_tooltip(&mut self, txt: &Text) {
         let dims = self.text_dims(&txt);
         // TODO Maybe also consider the cursor as a valid center
@@ -590,9 +590,13 @@ impl DrawBoth {
         g.redraw(&self.geom);
         g.unfork();
         for (txt, pt) in &self.txt {
-            g.draw_text_at_screenspace_topleft(
-                txt,
+            let dims = g.text_dims(&txt);
+            text::draw_text_bubble(
+                g,
                 ScreenPt::new(top_left.x + pt.x, top_left.y + pt.y),
+                txt,
+                dims,
+                true,
             );
         }
     }
diff --git a/ezgui/src/managed.rs b/ezgui/src/managed.rs
index 68a6298533..ff1195e7e2 100644
--- a/ezgui/src/managed.rs
+++ b/ezgui/src/managed.rs
@@ -707,9 +707,11 @@ impl Composite {
     }
 
     pub fn draw(&self, g: &mut GfxCtx) {
-        g.canvas.mark_covered_area(self.top_level.rect.clone());
-        if self.scrollable_x || self.scrollable_y {
-            g.enable_clipping(self.clip_rect.clone().unwrap());
+        if let Some(ref rect) = self.clip_rect {
+            g.enable_clipping(rect.clone());
+            g.canvas.mark_covered_area(rect.clone());
+        } else {
+            g.canvas.mark_covered_area(self.top_level.rect.clone());
         }
         self.top_level.draw(g, &self.sliders, &self.menus);
         if self.scrollable_x || self.scrollable_y {
diff --git a/ezgui/src/widgets/button.rs b/ezgui/src/widgets/button.rs
index 36a850e191..04afbbba1e 100644
--- a/ezgui/src/widgets/button.rs
+++ b/ezgui/src/widgets/button.rs
@@ -105,11 +105,6 @@ impl Button {
         } else {
             self.draw_normal.redraw(self.top_left, g);
         }
-
-        g.canvas
-            .covered_polygons
-            .borrow_mut()
-            .push(self.get_hitbox());
     }
 }
 
diff --git a/ezgui/src/widgets/modal_menu.rs b/ezgui/src/widgets/modal_menu.rs
index cfd5af3e68..53fec21907 100644
--- a/ezgui/src/widgets/modal_menu.rs
+++ b/ezgui/src/widgets/modal_menu.rs
@@ -196,7 +196,7 @@ impl ModalMenu {
     }
 
     pub fn draw(&self, g: &mut GfxCtx) {
-        g.draw_text_at_screenspace_topleft(&self.calculate_txt(), self.top_left);
+        g.draw_blocking_text_at_screenspace_topleft(&self.calculate_txt(), self.top_left);
     }
 
     fn recalculate_dims(&mut self, ctx: &EventCtx) {
diff --git a/ezgui/src/widgets/popup_menu.rs b/ezgui/src/widgets/popup_menu.rs
index 43b9fdc982..94a27a5af0 100644
--- a/ezgui/src/widgets/popup_menu.rs
+++ b/ezgui/src/widgets/popup_menu.rs
@@ -114,7 +114,7 @@ impl<T: Clone> PopupMenu<T> {
     }
 
     pub fn draw(&self, g: &mut GfxCtx) {
-        g.draw_text_at_screenspace_topleft(&self.calculate_txt(), self.top_left);
+        g.draw_blocking_text_at_screenspace_topleft(&self.calculate_txt(), self.top_left);
     }
 
     pub fn current_choice(&self) -> &T {
diff --git a/ezgui/src/widgets/slider.rs b/ezgui/src/widgets/slider.rs
index 45ce4d6a62..4a46518ab3 100644
--- a/ezgui/src/widgets/slider.rs
+++ b/ezgui/src/widgets/slider.rs
@@ -215,6 +215,8 @@ impl Slider {
 
     pub fn draw(&self, g: &mut GfxCtx) {
         self.draw.redraw(self.top_left, g);
+        // TODO Since the sliders in Composites are scrollbars outside of the clipping rectangle,
+        // this stays for now.
         g.canvas
             .mark_covered_area(ScreenRectangle::top_left(self.top_left, self.dims));
     }
diff --git a/ezgui/src/widgets/text_box.rs b/ezgui/src/widgets/text_box.rs
index ba8f9beb3a..4383abcf06 100644
--- a/ezgui/src/widgets/text_box.rs
+++ b/ezgui/src/widgets/text_box.rs
@@ -94,7 +94,7 @@ impl TextBox {
     }
 
     pub fn draw(&self, g: &mut GfxCtx) {
-        g.draw_text_at_screenspace_topleft(&self.get_text(), self.top_left);
+        g.draw_blocking_text_at_screenspace_topleft(&self.get_text(), self.top_left);
     }
 }