diff --git a/editor/src/ui.rs b/editor/src/ui.rs
index 1a78886958..e965f7a3e0 100644
--- a/editor/src/ui.rs
+++ b/editor/src/ui.rs
@@ -189,6 +189,9 @@ impl<S: UIState> GUI<RenderingHints> for UI<S> {
         {
             self.state.set_current_selection(self.mouseover_something());
         }
+        if input.window_lost_cursor() {
+            self.state.set_current_selection(None);
+        }
 
         let mut recalculate_current_selection = false;
         self.state.event(
diff --git a/ezgui/src/canvas.rs b/ezgui/src/canvas.rs
index fd464fab4f..73098b5710 100644
--- a/ezgui/src/canvas.rs
+++ b/ezgui/src/canvas.rs
@@ -15,8 +15,10 @@ pub struct Canvas {
     pub cam_y: f64,
     pub cam_zoom: f64,
 
+    // TODO We probably shouldn't even track screen-space cursor when we don't have the cursor.
     cursor_x: f64,
     cursor_y: f64,
+    window_has_cursor: bool,
 
     left_mouse_drag_from: Option<ScreenPt>,
 
@@ -47,6 +49,7 @@ impl Canvas {
 
             cursor_x: 0.0,
             cursor_y: 0.0,
+            window_has_cursor: true,
 
             left_mouse_drag_from: None,
             window_width: f64::from(initial_width),
@@ -82,6 +85,12 @@ impl Canvas {
             let delta = scroll * ZOOM_SPEED * self.cam_zoom;
             self.zoom_towards_mouse(delta);
         }
+        if input.window_gained_cursor() {
+            self.window_has_cursor = true;
+        }
+        if input.window_lost_cursor() {
+            self.window_has_cursor = false;
+        }
     }
 
     pub(crate) fn start_drawing(&self, g: &mut GfxCtx) {
@@ -169,7 +178,11 @@ impl Canvas {
     }
 
     pub fn get_cursor_in_map_space(&self) -> Option<Pt2D> {
-        Some(self.screen_to_map(self.get_cursor_in_screen_space()))
+        if self.window_has_cursor {
+            Some(self.screen_to_map(self.get_cursor_in_screen_space()))
+        } else {
+            None
+        }
     }
 
     pub fn screen_to_map(&self, pt: ScreenPt) -> Pt2D {
diff --git a/ezgui/src/event.rs b/ezgui/src/event.rs
index ef3f721a8d..cc6ef9c2b5 100644
--- a/ezgui/src/event.rs
+++ b/ezgui/src/event.rs
@@ -16,6 +16,8 @@ pub enum Event {
     // Time has passed; EventLoopMode::Animation is active
     Update,
     MouseMovedTo(ScreenPt),
+    WindowLostCursor,
+    WindowGainedCursor,
     // Vertical only
     MouseWheelScroll(f64),
     WindowResized(f64, f64),
@@ -24,8 +26,8 @@ pub enum Event {
 impl Event {
     pub fn from_piston_event(ev: pi::Event) -> Event {
         use piston::input::{
-            ButtonEvent, MouseCursorEvent, MouseScrollEvent, PressEvent, ReleaseEvent, ResizeEvent,
-            TouchEvent, UpdateEvent,
+            ButtonEvent, CursorEvent, MouseCursorEvent, MouseScrollEvent, PressEvent, ReleaseEvent,
+            ResizeEvent, TouchEvent, UpdateEvent,
         };
 
         if let Some(pi::Button::Mouse(button)) = ev.press_args() {
@@ -74,6 +76,14 @@ impl Event {
         if let Some(pair) = ev.resize_args() {
             return Event::WindowResized(f64::from(pair[0]), f64::from(pair[1]));
         }
+        if let Some(has) = ev.cursor_args() {
+            if has {
+                return Event::WindowGainedCursor;
+            } else {
+                // TODO Sometimes this doesn't happen! :(
+                return Event::WindowLostCursor;
+            }
+        }
 
         panic!("Unknown piston event {:?}", ev);
     }
diff --git a/ezgui/src/input.rs b/ezgui/src/input.rs
index bad799aa6f..812026e105 100644
--- a/ezgui/src/input.rs
+++ b/ezgui/src/input.rs
@@ -332,6 +332,13 @@ impl UserInput {
         self.event == Event::RightMouseButtonDown
     }
 
+    pub(crate) fn window_gained_cursor(&mut self) -> bool {
+        self.event == Event::WindowGainedCursor
+    }
+    pub fn window_lost_cursor(&mut self) -> bool {
+        self.event == Event::WindowLostCursor
+    }
+
     pub fn get_moved_mouse(&self) -> Option<ScreenPt> {
         if self.context_menu_active() {
             return None;
diff --git a/ezgui/src/runner.rs b/ezgui/src/runner.rs
index 73271b4782..bca0edc680 100644
--- a/ezgui/src/runner.rs
+++ b/ezgui/src/runner.rs
@@ -88,10 +88,9 @@ pub fn run<T, G: GUI<T>>(mut gui: G, window_title: &str) {
         } else {
             // Skip some events.
             use piston::input::{
-                AfterRenderEvent, CursorEvent, FocusEvent, IdleEvent, MouseRelativeEvent, TextEvent,
+                AfterRenderEvent, FocusEvent, IdleEvent, MouseRelativeEvent, TextEvent,
             };
             if ev.after_render_args().is_some()
-                || ev.cursor_args().is_some()
                 || ev.focus_args().is_some()
                 || ev.idle_args().is_some()
                 || ev.mouse_relative_args().is_some()