diff --git a/crates/ui-egui/src/chrome.rs b/crates/ui-egui/src/chrome.rs
index 032445d8..b30a0110 100644
--- a/crates/ui-egui/src/chrome.rs
+++ b/crates/ui-egui/src/chrome.rs
@@ -198,12 +198,15 @@ pub fn file_tabs(app: &mut CadApp, ui: &mut egui::Ui) {
             |ui: &mut egui::Ui, label: &str, dirty: bool, active: bool, closable: bool, w: f32, id: egui::Id| -> (bool, bool, egui::Response) {
                 let tr = Rect::from_min_size(pos2(x, r.top()), vec2(w, r.height()));
                 let resp = ui.interact(tr, id, Sense::click());
+                // The close button takes the tab's hover, so `resp.hovered()` would make the tab and
+                // its X flicker while the pointer is on the X.
+                let hovered = ui.rect_contains_pointer(tr);
                 ui.painter().rect_filled(
                     tr,
                     0.0,
                     if active {
                         t.tab_active
-                    } else if resp.hovered() {
+                    } else if hovered {
                         t.chrome
                     } else {
                         t.chrome_dark
@@ -223,7 +226,7 @@ pub fn file_tabs(app: &mut CadApp, ui: &mut egui::Ui) {
                 }
                 let resp = if cut { resp.on_hover_text(format!("{label}{mark}")) } else { resp };
                 let mut close = false;
-                if closable && (active || resp.hovered()) {
+                if closable && (active || hovered) {
                     let cr = Rect::from_center_size(pos2(tr.right() - 11.0, tr.center().y), vec2(12.0, 12.0));
                     let cresp = ui.interact(cr, id.with("x"), Sense::click());
                     icons::paint(ui.painter(), cr, Icon::Close, false);
diff --git a/crates/ui-egui/tests/file_tab_close.rs b/crates/ui-egui/tests/file_tab_close.rs
new file mode 100644
index 00000000..2e78b145
--- /dev/null
+++ b/crates/ui-egui/tests/file_tab_close.rs
@@ -0,0 +1,43 @@
+//! The close button of an inactive file tab stays while the pointer is on it, and a click on it
+//! closes that drawing. It used to take the tab's hover, so the next frame dropped it and the one
+//! after drew it again: the tab and its X flickered.
+
+use cadcraft_engine::Session;
+use cadcraft_ui_egui::{CadApp, Services};
+use egui::accesskit::Role;
+use egui::vec2;
+use egui_kittest::Harness;
+use egui_kittest::kittest::Queryable;
+
+#[test]
+fn an_inactive_tabs_close_button_stays_under_the_pointer_and_closes_it() {
+    let mut app = CadApp::new(Session::default(), Services::default());
+    app.run("new", serde_json::json!({})).unwrap();
+    app.run("new", serde_json::json!({})).unwrap();
+    app.ui.start_tab = false;
+    assert_ne!(app.session.active, 0, "the first drawing's tab is inactive");
+    let first = app.session.docs[0].title.clone();
+    let open = app.session.docs.len();
+    let mut h = Harness::builder().with_size(vec2(1200.0, 760.0)).build_ui_state(
+        |ui, app: &mut CadApp| {
+            app.logic(&ui.ctx().clone());
+            app.ui(ui);
+        },
+        app,
+    );
+    h.run_steps(5);
+    // Pointing at the tab shows its close button.
+    h.get_by_role_and_label(Role::Tab, &first).hover();
+    h.run_steps(3);
+    let close = format!("Close {first}");
+    h.get_by_label(&close).hover();
+    for frame in 0..6 {
+        h.step();
+        assert!(h.query_by_label(&close).is_some(), "the close button is gone on frame {frame} under the pointer");
+    }
+    h.get_by_label(&close).click();
+    h.run_steps(3);
+    let titles: Vec<&str> = h.state().session.docs.iter().map(|d| d.title.as_str()).collect();
+    assert_eq!(titles.len(), open - 1, "one drawing closed: {titles:?}");
+    assert!(!titles.contains(&first.as_str()), "the clicked tab's drawing is the one closed: {titles:?}");
+}