diff --git a/carousel.go b/carousel.go
index 05f4587..2b27b87 100644
--- a/carousel.go
+++ b/carousel.go
@@ -36,6 +36,8 @@ func (v CarouselView) Changed() bool { return v.changed }
 type carouselState struct {
 	paused bool
 	next   time.Time
+	// dotFocus leaves the arrows to the dots' focus group.
+	dotFocus bool
 }
 
 // Carousel shows slide *index of n with previous, next and position controls.
@@ -86,6 +88,7 @@ func Carousel(c *ui.Context, index *int, n int, opts CarouselOptions, slide func
 		c.After(st.next.Sub(now))
 	}
 	switch {
+	case st.dotFocus:
 	case v.Shortcut(0, ui.KeyLeft):
 		goTo(*index - 1)
 	case v.Shortcut(0, ui.KeyRight):
@@ -113,10 +116,17 @@ func Carousel(c *ui.Context, index *int, n int, opts CarouselOptions, slide func
 			}
 		})
 		ui.Row(c).Justify(ui.Center).AlignItems(ui.Center).Gap(u * 2).Children(func() {
+			st.dotFocus = false
 			ui.Row(c).Gap(u).FocusGroup(ui.Horizontal).Children(func() {
 				for i := range n {
-					if carouselDot(c, i, n, i == *index).Clicked() {
+					dot := carouselDot(c, i, n, i == *index)
+					if dot.Focused() {
+						st.dotFocus = true
+					}
+					// The arrows move the focus among the dots; the slide follows it.
+					if dot.Clicked() || dot.Focused() && i != *index {
 						goTo(i)
+						c.Invalidate()
 					}
 				}
 			})
diff --git a/carousel_test.go b/carousel_test.go
index aae5119..59d8435 100644
--- a/carousel_test.go
+++ b/carousel_test.go
@@ -146,3 +146,29 @@ func TestCarouselEmptyAutoplayKeys(t *testing.T) {
 		t.Fatalf("index %d", index)
 	}
 }
+
+func TestCarouselDotsFollowArrows(t *testing.T) {
+	h := &carouselHarness{}
+	tt := ui.NewTester(h.view, 420, 280)
+	for range 10 {
+		if tt.Focused("Slide 1 of 4") {
+			break
+		}
+		tt.Key(0, ui.KeyTab)
+	}
+	if !tt.Focused("Slide 1 of 4") {
+		t.Fatal("Tab never reached the first dot")
+	}
+	tt.Key(0, ui.KeyRight)
+	if h.index != 1 || !tt.Focused("Slide 2 of 4") {
+		t.Fatalf("Right: index %d, focus on dot 2 %v", h.index, tt.Focused("Slide 2 of 4"))
+	}
+	tt.Key(0, ui.KeyEnter)
+	if h.index != 1 {
+		t.Fatalf("Enter on the focused dot moved to %d", h.index)
+	}
+	tt.Key(0, ui.KeyEnd)
+	if h.index != 3 || !tt.Focused("Slide 4 of 4") {
+		t.Fatalf("End: index %d", h.index)
+	}
+}
diff --git a/data_table.go b/data_table.go
index 86ca4d6..508b20a 100644
--- a/data_table.go
+++ b/data_table.go
@@ -137,7 +137,7 @@ func DataTable[R any, K comparable](c *ui.Context, s *DataTableState[K], rows []
 			v.retry = dataPlaceholder(c, opts.Status, opts.Error, empty, msg(c, "list.empty"))
 			return
 		}
-		vis, cols := dataTableColumns(c, s, opts)
+		vis, cols := dataTableColumns(dataRowUnit(c), s, opts)
 		s.rows.Key = func(i int) any { return opts.Key(rows[view[i]]) }
 		s.rows.Label = func(i int) string { return opts.Columns[vis[0]].Text(rows[view[i]]) }
 		s.rows.Selected, s.rows.Sort, s.rows.Columns = &s.cursor, &s.Sort, s.Layout
@@ -146,7 +146,8 @@ func DataTable[R any, K comparable](c *ui.Context, s *DataTableState[K], rows []
 			s.rows.Selection = &s.Selection
 		}
 		// Rows reach the data-row height of the density.
-		restore := dataSelectTheme(c, d.ControlHeight()/8)
+		unit := dataRowUnit(c)
+		restore := dataSelectTheme(c, unit)
 		head := s.Sort
 		e := ui.Table(c, &s.rows, cols, len(view), func(row, col int) {
 			r := rows[view[row]]
@@ -265,8 +266,15 @@ func dataTableMenu[R any, K comparable](opts DataTableOptions[R, K]) []tableColu
 	return cols
 }
 
-func dataTableColumns[R any, K comparable](c *ui.Context, s *DataTableState[K], opts DataTableOptions[R, K]) ([]int, []ui.TableColumn) {
-	w := Density(c).ControlHeight()
+// dataRowUnit is the table spacing unit: rows reach the density's height and fit scaled text.
+func dataRowUnit(c *ui.Context) float32 {
+	// MyGo rows and the header are 8 units high with 1.5 units of padding above and below.
+	return max(Density(c).ControlHeight()/8, FontSize(c, theme.BodySize)*theme.LineHeight/5)
+}
+
+func dataTableColumns[R any, K comparable](unit float32, s *DataTableState[K], opts DataTableOptions[R, K]) ([]int, []ui.TableColumn) {
+	// The check box keeps its full hit width inside MyGo's 2.5-unit cell padding.
+	w := theme.MinHitSize + 5*unit
 	cols := []ui.TableColumn{{ID: dataTableMarkID, Width: w, Fixed: true, Align: ui.Center}}
 	var vis []int
 	for i, col := range opts.Columns {
diff --git a/data_table_test.go b/data_table_test.go
index dbbe47d..c153dee 100644
--- a/data_table_test.go
+++ b/data_table_test.go
@@ -26,6 +26,7 @@ type tableHarness struct {
 	changes  int
 	sorts    int
 	c        *ui.Context
+	density  theme.Density
 	seen     map[string]int
 }
 
@@ -44,7 +45,7 @@ func newTableHarness(rows []relic) *tableHarness {
 }
 
 func (h *tableHarness) view(c *ui.Context) {
-	Use(c, Settings{Mode: Light})
+	Use(c, Settings{Mode: Light, Density: h.density})
 	h.c, h.seen = c, map[string]int{}
 	ui.Column(c).Padding(10).Gap(8).Children(func() {
 		cols := h.opts
@@ -363,3 +364,40 @@ func TestDataTableSelectionColors(t *testing.T) {
 		t.Fatalf("selected row background %v, want Selection %v", got, want)
 	}
 }
+
+func TestDataTableCompactLargeText(t *testing.T) {
+	h := newTableHarness(relics())
+	h.opts.Multiple = true
+	h.density = theme.Compact
+	tt := ui.NewTester(h.view, 600, 700)
+	tt.SetPreferences(ui.Preferences{TextScale: 2})
+	head, _ := tt.Find("Name")
+	row, _ := tt.Find("Censer") // the first row, labeled by its first column
+	if head.Y+head.H > row.Y-1 {
+		t.Fatalf("header text %v runs past the header into row %v", head, row)
+	}
+	box, ok := tt.Find("Select row")
+	if !ok || box.W < theme.MinHitSize || box.H < theme.MinHitSize || box.X < row.X {
+		t.Fatalf("check box hit area %v in row %v", box, row)
+	}
+	if name, _ := tt.Find("Name"); box.X+box.W > name.X {
+		t.Fatalf("check box %v overlaps the Name column at %v", box, name.X)
+	}
+}
+
+func TestDataTableCheckBoxHitWidth(t *testing.T) {
+	for _, d := range []theme.Density{theme.Compact, theme.Default} {
+		h := newTableHarness(relics())
+		h.opts.Multiple = true
+		h.density = d
+		tt := ui.NewTester(h.view, 400, 360)
+		box, _ := tt.Find("Select row")
+		if box.W < theme.MinHitSize || box.H < theme.MinHitSize {
+			t.Fatalf("%v: check box hit area %v", d, box)
+		}
+		tt.ClickAt(box.X+1, box.Y+box.H/2) // its left edge still toggles
+		if h.st.Selection.Len() != 1 {
+			t.Fatalf("%v: left edge of the hit area missed", d)
+		}
+	}
+}
diff --git a/docs/components/071-data-table.md b/docs/components/071-data-table.md
index 1a3505e..68ab9d8 100644
--- a/docs/components/071-data-table.md
+++ b/docs/components/071-data-table.md
@@ -51,7 +51,7 @@ ui.Render(view, 400, 300, 1)
 
 ## 状态
 
-默认、表头悬停、排序箭头（升/降）、行悬停、选中行（Selection 背景 + Text 文字；单选首列 AccentText 菱形，多选首列勾选框）、聚焦（表格外焦点环）、加载、追加加载、失败、空、无匹配。数据行高度不低于当前密度的数据行高（28/36/44 DIP）。
+默认、表头悬停、排序箭头（升/降）、行悬停、选中行（Selection 背景 + Text 文字；单选首列 AccentText 菱形，多选首列勾选框）、聚焦（表格外焦点环）、加载、追加加载、失败、空、无匹配。数据行与表头高度不低于当前密度的数据行高（28/36/44 DIP），并随文本缩放增高；多选勾选框保留完整的 28 × 28 DIP 命中区域。
 
 ## 事件
 
diff --git a/docs/components/080-carousel.md b/docs/components/080-carousel.md
index 51cc923..e9db9e3 100644
--- a/docs/components/080-carousel.md
+++ b/docs/components/080-carousel.md
@@ -39,7 +39,7 @@ ui.Render(view, 400, 300, 1)
 ## 键盘操作
 
 - 焦点位于组件内时：←/→ 上一项、下一项；Home/End 第一项、最后一项。
-- 位置指示为一个焦点组：方向键在指示点间移动，Enter/Space 跳转。
+- 位置指示为一个焦点组：方向键在指示点间移动，当前项随焦点切换；此时方向键不再由整个组件处理。
 - Tab 依次到达上一项、下一项、位置指示与暂停按钮。
 
 ## 限制
diff --git a/testdata/snapshots/darwin/data_table-dark.png b/testdata/snapshots/darwin/data_table-dark.png
index cda8438..87ab18b 100644
Binary files a/testdata/snapshots/darwin/data_table-dark.png and b/testdata/snapshots/darwin/data_table-dark.png differ
diff --git a/testdata/snapshots/darwin/data_table-light.png b/testdata/snapshots/darwin/data_table-light.png
index ee748c6..a701a7a 100644
Binary files a/testdata/snapshots/darwin/data_table-light.png and b/testdata/snapshots/darwin/data_table-light.png differ
diff --git a/tree.go b/tree.go
index fb4796f..efd0c91 100644
--- a/tree.go
+++ b/tree.go
@@ -76,6 +76,15 @@ func (t *treeCore[K]) begin(label func(K) string, sel *ui.Selection[K], multiple
 	}
 }
 
+// clear drops the choice and row state when the tree has no items.
+func (t *treeCore[K]) clear(sel *ui.Selection[K]) {
+	var zero K
+	t.cursor, t.sel, t.has = -1, zero, false
+	sel.Clear()
+	clear(t.asked)
+	t.outline = ui.OutlineState[K]{Open: t.outline.Open}
+}
+
 // end reads a new choice, or finds the chosen item again after rows moved.
 func (t *treeCore[K]) end(c *ui.Context, changed bool) {
 	rows := t.outline.Rows()
@@ -178,6 +187,7 @@ func Tree[K comparable](c *ui.Context, s *TreeState[K], opts TreeOptions[K]) Tre
 	v.Element = ui.Column(c).MinHeight(0)
 	v.Children(func() {
 		if len(opts.Roots) == 0 {
+			t.clear(&s.Selection)
 			v.retry = dataPlaceholder(c, opts.Status, opts.Error, opts.Empty, msg(c, "list.empty"))
 			return
 		}
@@ -199,7 +209,9 @@ func Tree[K comparable](c *ui.Context, s *TreeState[K], opts TreeOptions[K]) Tre
 		v.changed, v.submitted = e.Changed(), e.Submitted()
 		v.retry = dataFooter(c, opts.Status, opts.Error)
 	})
-	t.end(c, v.changed)
+	if len(opts.Roots) > 0 {
+		t.end(c, v.changed)
+	}
 	if v.changed {
 		slog.Debug("mujica: tree changed", "row", t.cursor, "count", s.Selection.Len())
 	}
diff --git a/tree_table.go b/tree_table.go
index 6f09ab3..41e4ba7 100644
--- a/tree_table.go
+++ b/tree_table.go
@@ -124,6 +124,7 @@ func TreeTable[K comparable](c *ui.Context, s *TreeTableState[K], opts TreeTable
 	v.Element = ui.Column(c).MinHeight(0).Gap(d.Unit() * 2)
 	v.Children(func() {
 		if len(opts.Roots) == 0 {
+			t.clear(&s.Selection)
 			v.retry = dataPlaceholder(c, opts.Status, opts.Error, opts.Empty, msg(c, "list.empty"))
 			return
 		}
@@ -137,7 +138,7 @@ func TreeTable[K comparable](c *ui.Context, s *TreeTableState[K], opts TreeTable
 		roots := sorted(opts.Roots, &s.roots)
 		head := s.Sort
 		t.outline.List.Sort, t.outline.List.Columns = &s.Sort, s.Layout
-		restore := dataSelectTheme(c, d.ControlHeight()/8)
+		restore := dataSelectTheme(c, dataRowUnit(c))
 		e := ui.OutlineTable(c, &t.outline, cols, roots, children, func(item K, col int) {
 			if col > 0 {
 				opts.Columns[col].Cell(item)
@@ -160,7 +161,9 @@ func TreeTable[K comparable](c *ui.Context, s *TreeTableState[K], opts TreeTable
 		v.retry = dataFooter(c, opts.Status, opts.Error)
 	})
 	v.sorted = s.Sort != before
-	t.end(c, v.changed)
+	if len(opts.Roots) > 0 {
+		t.end(c, v.changed)
+	}
 	if v.sorted {
 		slog.Debug("mujica: tree_table sort", "column", s.Sort.Column, "descending", s.Sort.Descending)
 	}
diff --git a/tree_table_test.go b/tree_table_test.go
index 1013187..8a3c572 100644
--- a/tree_table_test.go
+++ b/tree_table_test.go
@@ -244,3 +244,20 @@ func TestTreeTableColumnMenuKeyboard(t *testing.T) {
 		t.Fatalf("rows not sorted by size: %s", got)
 	}
 }
+
+func TestTreeTableEmptyClearsSelection(t *testing.T) {
+	h := newTTHarness()
+	h.opts.Multiple = true
+	tt := ui.NewTester(h.view, 400, 360)
+	if err := tt.Click("Organ"); err != nil {
+		t.Fatal(err)
+	}
+	if k, ok := h.st.Selected(); !ok || k != "Organ" || h.st.Selection.Len() != 1 {
+		t.Fatalf("selected %q %v", k, ok)
+	}
+	h.opts.Roots = nil
+	tt.Frame()
+	if k, ok := h.st.Selected(); ok || h.st.Selection.Len() != 0 {
+		t.Fatalf("empty table still selects %q (%d chosen)", k, h.st.Selection.Len())
+	}
+}
diff --git a/tree_test.go b/tree_test.go
index 77354b2..e238b3a 100644
--- a/tree_test.go
+++ b/tree_test.go
@@ -252,3 +252,21 @@ func TestTreeSelectionFollowsLargeReorder(t *testing.T) {
 		t.Fatalf("after reversing: selected %d %v at row %d", k, ok, st.tree.cursor)
 	}
 }
+
+func TestTreeEmptyClearsSelection(t *testing.T) {
+	h := newTreeHarness()
+	tt := ui.NewTester(h.view, 400, 400)
+	if err := tt.Click("Sacristy"); err != nil {
+		t.Fatal(err)
+	}
+	h.opts.Roots = nil
+	tt.Frame()
+	if k, ok := h.st.Selected(); ok {
+		t.Fatalf("empty tree still selects %q", k)
+	}
+	h.opts.Roots = []string{"Nave", "Crypt", "Sacristy"}
+	tt.Frame()
+	if k, ok := h.st.Selected(); ok {
+		t.Fatalf("selection came back as %q", k)
+	}
+}