diff --git a/crates/chart/src/render.rs b/crates/chart/src/render.rs
index 3fa9f8431..3abf8bf14 100644
--- a/crates/chart/src/render.rs
+++ b/crates/chart/src/render.rs
@@ -141,6 +141,8 @@ fn needs_sanitizing(d: &ChartData) -> bool {
     let mut trendlines = 0usize;
     d.palette.len() > MAX_POINTS
         || long(d.categories.len())
+        || d.category_levels.len() > 3
+        || d.category_levels.iter().any(|l| l.len() > MAX_POINTS)
         || d.series.len() > MAX_SERIES
         || d.series.iter().any(|s| {
             trendlines += s.trendlines.len();
diff --git a/crates/chart/src/render/cartesian.rs b/crates/chart/src/render/cartesian.rs
index 6689bf202..44c7a3dc9 100644
--- a/crates/chart/src/render/cartesian.rs
+++ b/crates/chart/src/render/cartesian.rs
@@ -67,6 +67,10 @@ impl BarRun {
     fn new(pos: f32, lo: f32, hi: f32) -> Self {
         BarRun { bucket: pos.floor(), a0: pos, a1: pos, lo, hi, merged: false }
     }
+    /// Whether `lo..hi` touches the run's value span; a disjoint bar would be joined by a filled gap.
+    fn touches(&self, lo: f32, hi: f32) -> bool {
+        lo <= self.hi && hi >= self.lo
+    }
     fn add(&mut self, pos: f32, lo: f32, hi: f32) {
         self.merged = true;
         self.a0 = self.a0.min(pos);
@@ -135,7 +139,7 @@ impl BarSink {
             return;
         }
         match &mut self.run {
-            Some(m) if m.bucket == pos.floor() => m.add(pos, lo, lo + len),
+            Some(m) if m.bucket == pos.floor() && m.touches(lo, lo + len) => m.add(pos, lo, lo + len),
             run => {
                 if let Some(m) = run.replace(BarRun::new(pos, lo, lo + len)) {
                     m.draw(ctx, self.bw, self.horizontal, self.color, band);
diff --git a/crates/chart/src/tests/budget.rs b/crates/chart/src/tests/budget.rs
index 54d33aa7d..6c5a10879 100644
--- a/crates/chart/src/tests/budget.rs
+++ b/crates/chart/src/tests/budget.rs
@@ -158,6 +158,26 @@ fn clustered_hairline_series_keep_a_visible_strip() {
     }
 }
 
+#[test]
+fn stacked_hairline_bars_do_not_fill_the_gap_between_disjoint_spans() {
+    // Series 1 alternates +10 (stacked on the 100) and -10 (below zero): its two spans in one
+    // pixel column are 100..110 and -10..0, and the 100 units between them must stay empty.
+    let mut c = chart(ChartKind::ColumnStacked);
+    c.data_labels = false;
+    c.legend = LegendPos::None;
+    let mut d = data_of(2, 20_000);
+    for v in d.series[0].values.iter_mut() {
+        *v = Some(100.0);
+    }
+    for (i, v) in d.series[1].values.iter_mut().enumerate() {
+        *v = Some(if i % 2 == 0 { 10.0 } else { -10.0 });
+    }
+    let prims = render(&c, &d, 400.0, 300.0, &ApproxMeasure);
+    let rects = series_rects(&prims, d.series[1].color);
+    let tallest = rects.iter().map(|r| r.3).fold(0.0f32, f32::max);
+    assert!(!rects.is_empty() && tallest < 60.0, "tallest merged bar is {tallest} px");
+}
+
 #[test]
 fn clean_data_is_rendered_without_a_copy() {
     let d = data_of(3, 50);
@@ -181,6 +201,13 @@ fn clean_data_is_rendered_without_a_copy() {
     let got = sanitized(&many);
     assert_eq!(got.series.len(), 255);
     assert_eq!(*got, sanitize(&many));
+
+    // Too many category levels take the copying path too.
+    let mut levels = data_of(3, 50);
+    levels.category_levels = vec![vec!["a".into()]; 5];
+    let got = sanitized(&levels);
+    assert!(matches!(got, Cow::Owned(_)));
+    assert_eq!(got.category_levels.len(), 3);
 }
 
 #[test]
diff --git a/crates/chart/src/trend.rs b/crates/chart/src/trend.rs
index 6b22ed7ad..818c75796 100644
--- a/crates/chart/src/trend.rs
+++ b/crates/chart/src/trend.rs
@@ -294,7 +294,11 @@ pub(crate) fn moving_average(pts: &[(f64, f64)], period: u32) -> Vec<(f64, f64)>
     (p - 1..n)
         .filter_map(|i| {
             let s = i + 1 - p;
-            let sum = tail.get(s)? + if s.is_multiple_of(p) { 0.0 } else { *head.get(i)? };
+            let mut sum = tail.get(s)? + if s.is_multiple_of(p) { 0.0 } else { *head.get(i)? };
+            if !sum.is_finite() {
+                // A block sum overflowed although the window itself may not: sum it directly.
+                sum = pts.get(s..=i)?.iter().map(|q| q.1).sum();
+            }
             Some((pts.get(i)?.0, sum / p as f64))
         })
         .collect()
@@ -390,6 +394,15 @@ mod tests {
         }
     }
 
+    #[test]
+    fn moving_average_recomputes_a_window_whose_block_sums_overflow() {
+        let pts: Vec<(f64, f64)> = [0.0, -1e308, 1e308, 1e308, -1e308].iter().enumerate().map(|(i, y)| (i as f64, *y)).collect();
+        let fast = moving_average(&pts, 4);
+        let slow = moving_average_naive(&pts, 4);
+        assert_eq!(fast, slow);
+        assert!(fast.iter().all(|q| q.1.is_finite()));
+    }
+
     /// The trendline fit as it was written with a `Vec` of powers per data point.
     fn fit_reference(t: &Trendline, pts: &[(f64, f64)]) -> Option<TrendFit> {
         let kind = t.kind;