diff --git a/TASKS.md b/TASKS.md
index 59c1dd1..0728901 100644
--- a/TASKS.md
+++ b/TASKS.md
@@ -420,3 +420,4 @@ Per-component lines live in `tasks/`. Tags there:
 | T38a | 2 | PASS | |
 | T38b | 1 | PASS | |
 | T39a | 1 | FAIL | a larger text size cut the density strip at 280px; ten palette colors had no name; the density and sliders untested |
+| T39a | 2 | FAIL | segments split the strip equally and cut a longer label; the thumb lost its padding's height |
diff --git a/src/buttons/segmented.rs b/src/buttons/segmented.rs
index 2e59da1..7ee2d4d 100644
--- a/src/buttons/segmented.rs
+++ b/src/buttons/segmented.rs
@@ -110,8 +110,9 @@ impl RenderOnce for SegmentedControl {
              }| {
                 div()
                     .absolute()
-                    .top_0p5()
-                    .bottom_0p5()
+                    .top_0()
+                    .bottom_0()
+                    .debug_selector(|| "segment-thumb".into())
                     .rounded(theme.radius(Radius::Md))
                     .bg(colors.surface)
                     .border_1()
@@ -135,13 +136,13 @@ impl RenderOnce for SegmentedControl {
                 let on = ix == chosen;
                 let fg = if on { colors.fg } else { colors.fg_muted };
                 let (focus, reveal) = stops.remove(0);
-                let named = value.clone();
+                let (named, labeled) = (value.clone(), value.clone());
                 let (change, measure) = (self.on_change.clone(), state.clone());
                 let segment = div()
                     .id(("segment", ix))
                     .relative()
                     .flex()
-                    .flex_1()
+                    .flex_auto()
                     .min_w_0()
                     .items_center()
                     .justify_center()
@@ -176,15 +177,20 @@ impl RenderOnce for SegmentedControl {
                         segment.child(Icon::new(icon).size(icon_size).color(fg))
                     })
                     .when(!label.is_empty(), |segment| {
-                        segment.child(div().min_w_0().child(Ellipsis::new(label)))
-                    })
-                    .child(measure_item(measure, ix, Axis::Horizontal));
+                        segment.child(
+                            div()
+                                .min_w_0()
+                                .debug_selector(move || format!("segment-label {labeled}"))
+                                .child(Ellipsis::new(label)),
+                        )
+                    });
                 div()
                     .relative()
                     .flex()
-                    .flex_1()
+                    .flex_auto()
                     .min_w_0()
                     .child(segment)
+                    .child(measure_item(measure, ix, Axis::Horizontal))
                     .child(reveal)
             });
         let control = div()
diff --git a/src/settings/tests/theme.rs b/src/settings/tests/theme.rs
index 4c12ef2..8b50931 100644
--- a/src/settings/tests/theme.rs
+++ b/src/settings/tests/theme.rs
@@ -118,3 +118,36 @@ fn the_density_strip_fits_a_narrow_box_with_larger_text(cx: &mut TestAppContext)
         .expect("the last segment");
     assert!(last.right() <= frame.right(), "{last:?} inside {frame:?}");
 }
+
+/// At 280px and the base size the strip has room, so each label keeps its whole width: eleven letters to seven.
+#[gpui::test]
+fn a_label_gives_way_only_when_the_strip_lacks_room(cx: &mut TestAppContext) {
+    let (_, cx) = desk(narrow, cx);
+    settle(cx);
+    let compact = cx
+        .debug_bounds("segment-label Compact")
+        .expect("Compact's label");
+    let comfortable = cx
+        .debug_bounds("segment-label Comfortable")
+        .expect("Comfortable's label");
+    let ratio = comfortable.size.width / compact.size.width;
+    assert!(
+        (ratio - 11.0 / 7.0).abs() < 0.01,
+        "{comfortable:?} to {compact:?}"
+    );
+}
+
+/// The thumb covers the chosen segment, top to bottom and side to side.
+#[gpui::test]
+fn the_thumb_covers_the_chosen_segment(cx: &mut TestAppContext) {
+    let (_, cx) = desk(editor, cx);
+    for _ in 0..3 {
+        std::thread::sleep(std::time::Duration::from_millis(2));
+        settle(cx);
+    }
+    let thumb = cx.debug_bounds("segment-thumb").expect("the thumb");
+    let chosen = cx
+        .debug_bounds("segment Standard")
+        .expect("the chosen segment");
+    assert_eq!(thumb, chosen);
+}