diff --git a/crates/egui/src/containers/area.rs b/crates/egui/src/containers/area.rs
index 9d4ed44dedb..df9e9db8668 100644
--- a/crates/egui/src/containers/area.rs
+++ b/crates/egui/src/containers/area.rs
@@ -525,20 +525,11 @@ impl Prepared {
             enabled: _,
             constrain: _,
             constrain_rect: _,
-            sizing_pass,
+            sizing_pass: _,
         } = self;
 
         state.size = content_ui.min_size();
 
-        if sizing_pass {
-            // If during the sizing pass we measure our width to `123.45` and
-            // then try to wrap to exactly that next frame,
-            // we may accidentally wrap the last letter of some text.
-            // We only do this after the initial sizing pass though;
-            // otherwise we could end up with for-ever expanding areas.
-            state.size = state.size.ceil();
-        }
-
         ctx.memory_mut(|m| m.areas_mut().set_state(layer_id, state));
 
         move_response
diff --git a/crates/egui/src/containers/popup.rs b/crates/egui/src/containers/popup.rs
index f0c82819728..ed2a15989ac 100644
--- a/crates/egui/src/containers/popup.rs
+++ b/crates/egui/src/containers/popup.rs
@@ -1,49 +1,8 @@
 //! Show popup windows, tooltips, context menus etc.
 
-use crate::*;
-
-// ----------------------------------------------------------------------------
-
-/// Same state for all tooltips.
-#[derive(Clone, Debug, Default)]
-pub(crate) struct TooltipState {
-    last_common_id: Option<Id>,
-    individual_ids_and_sizes: ahash::HashMap<usize, (Id, Vec2)>,
-}
-
-impl TooltipState {
-    pub fn load(ctx: &Context) -> Option<Self> {
-        ctx.data_mut(|d| d.get_temp(Id::NULL))
-    }
-
-    fn store(self, ctx: &Context) {
-        ctx.data_mut(|d| d.insert_temp(Id::NULL, self));
-    }
+use frame_state::PerWidgetTooltipState;
 
-    fn individual_tooltip_size(&self, common_id: Id, index: usize) -> Option<Vec2> {
-        if self.last_common_id == Some(common_id) {
-            Some(self.individual_ids_and_sizes.get(&index)?.1)
-        } else {
-            None
-        }
-    }
-
-    fn set_individual_tooltip(
-        &mut self,
-        common_id: Id,
-        index: usize,
-        individual_id: Id,
-        size: Vec2,
-    ) {
-        if self.last_common_id != Some(common_id) {
-            self.last_common_id = Some(common_id);
-            self.individual_ids_and_sizes.clear();
-        }
-
-        self.individual_ids_and_sizes
-            .insert(index, (individual_id, size));
-    }
-}
+use crate::*;
 
 // ----------------------------------------------------------------------------
 
@@ -94,10 +53,8 @@ pub fn show_tooltip_at_pointer<R>(
     id: Id,
     add_contents: impl FnOnce(&mut Ui) -> R,
 ) -> Option<R> {
-    let suggested_pos = ctx
-        .input(|i| i.pointer.hover_pos())
-        .map(|pointer_pos| pointer_pos + vec2(16.0, 16.0));
-    show_tooltip_at(ctx, id, suggested_pos, add_contents)
+    ctx.input(|i| i.pointer.hover_pos())
+        .map(|pointer_pos| show_tooltip_at(ctx, id, pointer_pos + vec2(16.0, 16.0), add_contents))
 }
 
 /// Show a tooltip under the given area.
@@ -106,21 +63,16 @@ pub fn show_tooltip_at_pointer<R>(
 pub fn show_tooltip_for<R>(
     ctx: &Context,
     id: Id,
-    rect: &Rect,
+    widget_rect: &Rect,
     add_contents: impl FnOnce(&mut Ui) -> R,
-) -> Option<R> {
-    let expanded_rect = rect.expand2(vec2(2.0, 4.0));
-    let (above, position) = if ctx.input(|i| i.any_touches()) {
-        (true, expanded_rect.left_top())
-    } else {
-        (false, expanded_rect.left_bottom())
-    };
+) -> R {
+    let is_touch_screen = ctx.input(|i| i.any_touches());
+    let allow_placing_below = !is_touch_screen; // There is a finger below.
     show_tooltip_at_avoid_dyn(
         ctx,
         id,
-        Some(position),
-        above,
-        expanded_rect,
+        allow_placing_below,
+        widget_rect,
         Box::new(add_contents),
     )
 }
@@ -131,101 +83,119 @@ pub fn show_tooltip_for<R>(
 pub fn show_tooltip_at<R>(
     ctx: &Context,
     id: Id,
-    suggested_position: Option<Pos2>,
+    suggested_position: Pos2,
     add_contents: impl FnOnce(&mut Ui) -> R,
-) -> Option<R> {
-    let above = false;
-    show_tooltip_at_avoid_dyn(
-        ctx,
-        id,
-        suggested_position,
-        above,
-        Rect::NOTHING,
-        Box::new(add_contents),
-    )
+) -> R {
+    let allow_placing_below = true;
+    let rect = Rect::from_center_size(suggested_position, Vec2::ZERO);
+    show_tooltip_at_avoid_dyn(ctx, id, allow_placing_below, &rect, Box::new(add_contents))
 }
 
 fn show_tooltip_at_avoid_dyn<'c, R>(
     ctx: &Context,
-    individual_id: Id,
-    suggested_position: Option<Pos2>,
-    above: bool,
-    mut avoid_rect: Rect,
+    widget_id: Id,
+    allow_placing_below: bool,
+    widget_rect: &Rect,
     add_contents: Box<dyn FnOnce(&mut Ui) -> R + 'c>,
-) -> Option<R> {
-    let spacing = 4.0;
-
+) -> R {
     // if there are multiple tooltips open they should use the same common_id for the `tooltip_size` caching to work.
-    let mut frame_state =
-        ctx.frame_state(|fs| fs.tooltip_state)
-            .unwrap_or(crate::frame_state::TooltipFrameState {
-                common_id: individual_id,
-                rect: Rect::NOTHING,
-                count: 0,
-            });
+    let mut state = ctx.frame_state(|fs| {
+        fs.tooltip_state
+            .widget_tooltips
+            .get(&widget_id)
+            .copied()
+            .unwrap_or(PerWidgetTooltipState {
+                bounding_rect: *widget_rect,
+                tooltip_count: 0,
+            })
+    });
 
-    let mut position = if frame_state.rect.is_positive() {
-        avoid_rect = avoid_rect.union(frame_state.rect);
-        if above {
-            frame_state.rect.left_top() - spacing * Vec2::Y
-        } else {
-            frame_state.rect.left_bottom() + spacing * Vec2::Y
-        }
-    } else if let Some(position) = suggested_position {
-        position
-    } else if ctx.memory(|mem| mem.everything_is_visible()) {
-        Pos2::ZERO
-    } else {
-        return None; // No good place for a tooltip :(
-    };
+    let tooltip_area_id = tooltip_id(widget_id, state.tooltip_count);
+    let expected_tooltip_size =
+        AreaState::load(ctx, tooltip_area_id).map_or(vec2(64.0, 32.0), |area| area.size);
 
-    let mut long_state = TooltipState::load(ctx).unwrap_or_default();
-    let expected_size =
-        long_state.individual_tooltip_size(frame_state.common_id, frame_state.count);
-    let expected_size = expected_size.unwrap_or_else(|| vec2(64.0, 32.0));
+    let screen_rect = ctx.screen_rect();
 
-    if above {
-        position.y -= expected_size.y;
-    }
+    let (pivot, anchor) = find_tooltip_position(
+        screen_rect,
+        state.bounding_rect,
+        allow_placing_below,
+        expected_tooltip_size,
+    );
 
-    position = position.at_most(ctx.screen_rect().max - expected_size);
+    let InnerResponse { inner, response } = Area::new(tooltip_area_id)
+        .order(Order::Tooltip)
+        .pivot(pivot)
+        .fixed_pos(anchor)
+        .default_width(ctx.style().spacing.tooltip_width)
+        .constrain_to(screen_rect)
+        .interactable(false)
+        .show(ctx, |ui| {
+            Frame::popup(&ctx.style()).show_dyn(ui, add_contents).inner
+        });
 
-    // check if we intersect the avoid_rect
-    {
-        let new_rect = Rect::from_min_size(position, expected_size);
+    state.tooltip_count += 1;
+    state.bounding_rect = state.bounding_rect.union(response.rect);
+    ctx.frame_state_mut(|fs| fs.tooltip_state.widget_tooltips.insert(widget_id, state));
 
-        // Note: We use shrink so that we don't get false positives when the rects just touch
-        if new_rect.shrink(1.0).intersects(avoid_rect) {
-            if above {
-                // place below instead:
-                position = avoid_rect.left_bottom() + spacing * Vec2::Y;
-            } else {
-                // place above instead:
-                position = Pos2::new(position.x, avoid_rect.min.y - expected_size.y - spacing);
-            }
-        }
-    }
+    inner
+}
 
-    let position = position.at_least(ctx.screen_rect().min);
+fn tooltip_id(widget_id: Id, tooltip_count: usize) -> Id {
+    widget_id.with(tooltip_count)
+}
 
-    let area_id = frame_state.common_id.with(frame_state.count);
+/// Returns `(PIVOT, POS)` to mean: put the `PIVOT` corner of the tooltip at `POS`.
+///
+/// Note: the position might need to be constrained to the screen,
+/// (e.g. moved sideways if shown under the widget)
+/// but the `Area` will take care of that.
+fn find_tooltip_position(
+    screen_rect: Rect,
+    widget_rect: Rect,
+    allow_placing_below: bool,
+    tooltip_size: Vec2,
+) -> (Align2, Pos2) {
+    let spacing = 4.0;
 
-    let InnerResponse { inner, response } =
-        show_tooltip_area_dyn(ctx, area_id, position, add_contents);
+    // Does it fit below?
+    if allow_placing_below
+        && widget_rect.bottom() + spacing + tooltip_size.y <= screen_rect.bottom()
+    {
+        return (
+            Align2::LEFT_TOP,
+            widget_rect.left_bottom() + spacing * Vec2::DOWN,
+        );
+    }
 
-    long_state.set_individual_tooltip(
-        frame_state.common_id,
-        frame_state.count,
-        individual_id,
-        response.rect.size(),
-    );
-    long_state.store(ctx);
+    // Does it fit above?
+    if screen_rect.top() + tooltip_size.y + spacing <= widget_rect.top() {
+        return (
+            Align2::LEFT_BOTTOM,
+            widget_rect.left_top() + spacing * Vec2::UP,
+        );
+    }
 
-    frame_state.count += 1;
-    frame_state.rect = frame_state.rect.union(response.rect);
-    ctx.frame_state_mut(|fs| fs.tooltip_state = Some(frame_state));
+    // Does it fit to the right?
+    if widget_rect.right() + spacing + tooltip_size.x <= screen_rect.right() {
+        return (
+            Align2::LEFT_TOP,
+            widget_rect.right_top() + spacing * Vec2::RIGHT,
+        );
+    }
 
-    Some(inner)
+    // Does it fit to the left?
+    if screen_rect.left() + tooltip_size.x + spacing <= widget_rect.left() {
+        return (
+            Align2::RIGHT_TOP,
+            widget_rect.left_top() + spacing * Vec2::LEFT,
+        );
+    }
+
+    // It doesn't fit anywhere :(
+
+    // Just show it anyway:
+    (Align2::LEFT_TOP, screen_rect.left_top())
 }
 
 /// Show some text at the current pointer position (if any).
@@ -249,42 +219,13 @@ pub fn show_tooltip_text(ctx: &Context, id: Id, text: impl Into<WidgetText>) ->
     })
 }
 
-/// Show a pop-over window.
-fn show_tooltip_area_dyn<'c, R>(
-    ctx: &Context,
-    area_id: Id,
-    window_pos: Pos2,
-    add_contents: Box<dyn FnOnce(&mut Ui) -> R + 'c>,
-) -> InnerResponse<R> {
-    use containers::*;
-    Area::new(area_id)
-        .order(Order::Tooltip)
-        .fixed_pos(window_pos)
-        .default_width(ctx.style().spacing.tooltip_width)
-        .constrain_to(ctx.screen_rect())
-        .interactable(false)
-        .show(ctx, |ui| {
-            Frame::popup(&ctx.style()).show_dyn(ui, add_contents).inner
-        })
-}
-
 /// Was this popup visible last frame?
-pub fn was_tooltip_open_last_frame(ctx: &Context, tooltip_id: Id) -> bool {
-    if let Some(state) = TooltipState::load(ctx) {
-        if let Some(common_id) = state.last_common_id {
-            for (count, (individual_id, _size)) in &state.individual_ids_and_sizes {
-                if *individual_id == tooltip_id {
-                    let area_id = common_id.with(count);
-                    let layer_id = LayerId::new(Order::Tooltip, area_id);
-                    if ctx.memory(|mem| mem.areas().visible_last_frame(&layer_id)) {
-                        return true;
-                    }
-                }
-            }
-        }
-    }
-
-    false
+pub fn was_tooltip_open_last_frame(ctx: &Context, widget_id: Id) -> bool {
+    let primary_tooltip_area_id = tooltip_id(widget_id, 0);
+    ctx.memory(|mem| {
+        mem.areas()
+            .visible_last_frame(&LayerId::new(Order::Tooltip, primary_tooltip_area_id))
+    })
 }
 
 /// Helper for [`popup_above_or_below_widget`].
diff --git a/crates/egui/src/frame_state.rs b/crates/egui/src/frame_state.rs
index e1414bba166..28c8c364b78 100644
--- a/crates/egui/src/frame_state.rs
+++ b/crates/egui/src/frame_state.rs
@@ -1,10 +1,23 @@
 use crate::{id::IdSet, *};
 
-#[derive(Clone, Copy, Debug)]
+#[derive(Clone, Debug, Default)]
 pub(crate) struct TooltipFrameState {
-    pub common_id: Id,
-    pub rect: Rect,
-    pub count: usize,
+    pub widget_tooltips: IdMap<PerWidgetTooltipState>,
+}
+
+impl TooltipFrameState {
+    pub(crate) fn clear(&mut self) {
+        self.widget_tooltips.clear();
+    }
+}
+
+#[derive(Clone, Copy, Debug)]
+pub(crate) struct PerWidgetTooltipState {
+    /// Bounding rectangle for all widget and all previous tooltips.
+    pub bounding_rect: Rect,
+
+    /// How many tooltips have been shown for this widget this frame?
+    pub tooltip_count: usize,
 }
 
 #[cfg(feature = "accesskit")]
@@ -35,8 +48,8 @@ pub(crate) struct FrameState {
 
     /// If a tooltip has been shown this frame, where was it?
     /// This is used to prevent multiple tooltips to cover each other.
-    /// Initialized to `None` at the start of each frame.
-    pub(crate) tooltip_state: Option<TooltipFrameState>,
+    /// Reset at the start of each frame.
+    pub(crate) tooltip_state: TooltipFrameState,
 
     /// The current scroll area should scroll to this range (horizontal, vertical).
     pub(crate) scroll_target: [Option<(Rangef, Option<Align>)>; 2],
@@ -72,7 +85,7 @@ impl Default for FrameState {
             available_rect: Rect::NAN,
             unused_rect: Rect::NAN,
             used_by_panels: Rect::NAN,
-            tooltip_state: None,
+            tooltip_state: Default::default(),
             scroll_target: [None, None],
             scroll_delta: Vec2::default(),
             #[cfg(feature = "accesskit")]
@@ -110,7 +123,7 @@ impl FrameState {
         *available_rect = screen_rect;
         *unused_rect = screen_rect;
         *used_by_panels = Rect::NOTHING;
-        *tooltip_state = None;
+        tooltip_state.clear();
         *scroll_target = [None, None];
         *scroll_delta = Vec2::default();