diff --git a/crates/render/src/hatch.rs b/crates/render/src/hatch.rs
index 880322fb5..6b96d70ca 100644
--- a/crates/render/src/hatch.rs
+++ b/crates/render/src/hatch.rs
@@ -510,6 +510,12 @@ impl Family<'_> {
 
     /// Intersect a pattern family with boundary loops, respecting view, output, cancellation, and shared dash-work limits.
     fn sweep(&self, loops: &[Vec<Vec2>], px: f64, view: Option<&Bounds2>, cancel: Option<&AtomicBool>, out: &mut Vec<Vec<Vec2>>, work: &mut u64) {
+        // Transforming the boundary is charged before it is done, at the scanline rate (one unit per 8 vertices).
+        let verts: u64 = loops.iter().map(|l| l.len() as u64).sum();
+        if *work == 0 {
+            return;
+        }
+        *work = work.saturating_sub(verts / 8 + 1);
         let local: Vec<Vec<Vec2>> = loops.iter().map(|l| l.iter().map(|p| self.to_local(*p)).collect()).collect();
         let bb = Bounds2::from_points(local.iter().flatten().copied());
         if bb.is_empty() {
diff --git a/crates/render/src/linetype_text.rs b/crates/render/src/linetype_text.rs
index 8770eb087..84293ba5f 100644
--- a/crates/render/src/linetype_text.rs
+++ b/crates/render/src/linetype_text.rs
@@ -102,7 +102,13 @@ fn elements(d: &Drawing, lt: &Linetype, scale: f64) -> Vec<Element> {
         };
         let (local, _) = cadcraft_fonts::place(&font, text, &params);
         let finite = |v: f64| if v.is_finite() { v } else { 0.0 };
-        let points = local.strokes.iter().map(Vec::len).sum::<usize>() + local.glyphs.iter().flatten().map(Vec::len).sum::<usize>();
+        // Points plus one per stroke and glyph slot, and one for the label itself, so a label of empty
+        // glyphs still has a cost proportional to its size.
+        let points = local.strokes.iter().map(Vec::len).sum::<usize>()
+            + local.glyphs.iter().flatten().map(Vec::len).sum::<usize>()
+            + local.strokes.len()
+            + local.glyphs.len()
+            + 1;
         out.push(Element {
             at,
             points,