diff --git a/crates/ui-egui/src/canvas.rs b/crates/ui-egui/src/canvas.rs
index 85412cb53d..d8b415f922 100644
--- a/crates/ui-egui/src/canvas.rs
+++ b/crates/ui-egui/src/canvas.rs
@@ -70,7 +70,7 @@ pub use selection_marks::SelectionMarks;
 #[cfg(test)]
 pub(crate) use task_bar::chip_paints;
 use task_bar::task_bar;
-pub(crate) use task_bar::{has_colors, task_bar_rect, task_bar_shows_type};
+pub(crate) use task_bar::{has_colors, task_bar_rect, task_bar_shows_fonts, task_bar_shows_type};
 #[cfg(test)]
 use tool_overlays::{DIAL_RADIUS, HiddenMarks};
 pub use tool_overlays::{HiddenChars, SpellingMarks};
diff --git a/crates/ui-egui/src/canvas/task_bar.rs b/crates/ui-egui/src/canvas/task_bar.rs
index c0422e0347..e908640c25 100644
--- a/crates/ui-egui/src/canvas/task_bar.rs
+++ b/crates/ui-egui/src/canvas/task_bar.rs
@@ -13,6 +13,12 @@ pub(crate) fn task_bar_rect(ctx: &egui::Context) -> Option<egui::Rect> {
     ctx.memory(|m| m.areas().is_visible(&egui::LayerId::new(egui::Order::Middle, id)).then(|| m.area_rect(id)).flatten())
 }
 
+/// Whether the Contextual Task Bar, where it was last drawn, held the font controls: on a canvas
+/// too narrow for them it leaves them out.
+pub(crate) fn task_bar_shows_fonts(ctx: &egui::Context) -> bool {
+    task_bar_rect(ctx).is_some() && ctx.data(|d| d.get_temp::<bool>(task_bar_id().with("fonts")).unwrap_or(false))
+}
+
 /// Whether the objects `ids` (or anything inside them) are painted with a colour: a solid colour,
 /// a gradient's stops or a mesh's points, which Recolor Artwork can change.
 pub(crate) fn has_colors(doc: &vectorcraft_doc::Document, ids: &[vectorcraft_doc::NodeId]) -> bool {
@@ -235,6 +241,7 @@ pub(super) fn task_bar(app: &mut VectorcraftApp, ui: &mut Ui, xf: &Xf) {
     let bounds = xf.rect.shrink(8.0);
     // On a canvas too narrow for the type controls at their narrowest, the bar leaves them out.
     let fonts = fonts && bounds.width() - 18.0 >= crate::panels::character::task_bar_min_room();
+    ui.ctx().data_mut(|d| d.insert_temp(task_bar_id().with("fonts"), fonts));
     // The width of the bar's frame (margins and stroke), its handle, Fill and Stroke chips,
     // Recolor Artwork, Lock or Shape Properties, and More Options, each after a 6-point gap.
     let chips: f32 =
diff --git a/crates/ui-egui/src/font_menu.rs b/crates/ui-egui/src/font_menu.rs
index 01e4d9e524..0bf87a88cd 100644
--- a/crates/ui-egui/src/font_menu.rs
+++ b/crates/ui-egui/src/font_menu.rs
@@ -70,7 +70,12 @@ impl WheelOwner {
             Self::ControlPopover(anchor) => {
                 return app.ui.control_bar && app.ui.screen_mode < 2 && widgets::popover_is_open(ctx, anchor);
             }
-            Self::TaskBar => return crate::canvas::task_bar_shows_type(app) && crate::canvas::task_bar_rect(ctx).is_some(),
+            Self::TaskBar => {
+                return app.ui.task_bar
+                    && app.ui.screen_mode < 3
+                    && crate::canvas::task_bar_shows_type(app)
+                    && crate::canvas::task_bar_shows_fonts(ctx);
+            }
             Self::Character => "character",
             Self::Properties => {
                 let selected = app.session.active().and_then(|document| document.selection.objects.first().and_then(|id| document.doc.node(*id)));
diff --git a/crates/ui-egui/src/tests/taskbar.rs b/crates/ui-egui/src/tests/taskbar.rs
index 202d6eb4c1..58f42b57a2 100644
--- a/crates/ui-egui/src/tests/taskbar.rs
+++ b/crates/ui-egui/src/tests/taskbar.rs
@@ -769,6 +769,47 @@ fn selected_types_font_controls_take_a_second_row_on_a_narrow_canvas() {
     assert!(canvas.contains_rect(r) && r.height() < 60.0, "no font controls on a 160 px screen: {r:?} in {canvas:?}");
 }
 
+/// When the canvas narrows so far that the bar leaves its font controls out, the font family
+/// field it drew before no longer takes the mouse wheel.
+#[test]
+fn a_task_bar_without_its_font_controls_leaves_their_wheel() {
+    let mut app = app();
+    app.run("tool.select", json!({"tool": "type"})).unwrap();
+    app.run("text.create", json!({"x": 20, "y": 60, "text": "Hello", "size": 20})).unwrap();
+    app.session.apply_actions(vec![vectorcraft_tools::Action::Notify("text.editNew".into())]).unwrap();
+    let ctx = egui::Context::default();
+    crate::theme::install_fonts(&ctx);
+    let draw = |app: &mut VectorcraftApp, width: f32| {
+        let screen = Rect::from_min_size(Pos2::ZERO, vec2(width, 700.0));
+        for _ in 0..3 {
+            let mut out = ctx.run_ui(egui::RawInput { screen_rect: Some(screen), ..Default::default() }, |ui| canvas::show(app, ui));
+            out.textures_delta.clear();
+        }
+    };
+    draw(&mut app, 1000.0);
+    let bar = canvas::task_bar_rect(&ctx).expect("the task bar shows");
+    let viewport = egui::ViewportId::ROOT;
+    let points = (0..(bar.width() / 4.0) as usize).flat_map(|x| (0..(bar.height() / 4.0) as usize).map(move |y| (x, y)));
+    let field = points
+        .map(|(x, y)| bar.min + vec2(x as f32 * 4.0, y as f32 * 4.0))
+        .find(|p| crate::font_menu::wheel_field_layer_for_test(&ctx, viewport, *p).is_some())
+        .expect("the bar's font family field takes the wheel");
+    draw(&mut app, 160.0);
+    assert!(canvas::task_bar_rect(&ctx).is_some(), "the bar still shows, without its font controls");
+    crate::font_menu::sync_wheel_target(&app, &ctx, viewport);
+    assert!(crate::font_menu::wheel_field_layer_for_test(&ctx, viewport, field).is_none(), "the left-out field at {field:?} still takes the wheel");
+
+    // Hiding the bar (Window › Contextual Task Bar) releases the field before the next layout.
+    draw(&mut app, 1000.0);
+    assert!(crate::font_menu::wheel_field_layer_for_test(&ctx, viewport, field).is_some(), "the field is back");
+    app.run("window.taskBar", json!({})).unwrap();
+    crate::font_menu::sync_wheel_target(&app, &ctx, viewport);
+    assert!(
+        crate::font_menu::wheel_field_layer_for_test(&ctx, viewport, field).is_none(),
+        "the hidden bar's field at {field:?} still takes the wheel"
+    );
+}
+
 /// While a Type tool edits type, the Fill chip shows the selected characters' fill, and "?" where
 /// their fills differ.
 #[test]