diff --git a/crates/affinity/src/geometry.rs b/crates/affinity/src/geometry.rs
index 945c3040f..bb1c45746 100644
--- a/crates/affinity/src/geometry.rs
+++ b/crates/affinity/src/geometry.rs
@@ -178,6 +178,10 @@ const MAX_PRESSURE_SEGMENTS: usize = 256;
 /// points; the document's limit counts all of them.
 const PRESSURE_POINTS: usize = 512;
 
+/// Most points one pressure curve can have (see [`PRESSURE_POINTS`]). A curve that can't be read
+/// counts this many against the document's limit.
+pub(crate) const MAX_PRESSURE_CURVE_POINTS: usize = 1 + 4 * MAX_PRESSURE_SEGMENTS;
+
 /// A stroke's pressure curve (`LDsc.LDeP`, a `CrvD` whose positional `Data` holds an array of
 /// 18-byte records as in [`curves`]): x is the position along the path (0 to 1) and y the width as
 /// a fraction of the stroke's weight. Each segment is sampled at 2 to 8 points, at most
diff --git a/crates/affinity/src/paint.rs b/crates/affinity/src/paint.rs
index cfc95b8dd..12102581e 100644
--- a/crates/affinity/src/paint.rs
+++ b/crates/affinity/src/paint.rs
@@ -357,8 +357,9 @@ pub(crate) fn stroke(r: &mut Reader, pen: ObjId, ldsc: ObjId, local: Affine, beh
         r.warn("brush strokes (imported as plain strokes)");
     }
     // The pressure curve sets the width along the path; one at full width all along is a plain
-    // stroke. Every curve read, full width or not, counts against the document's points, and once
-    // they are used up the rest are not read.
+    // stroke. Every curve read counts against the document's points: one at full width counts its
+    // points, and one that can't be read counts the most a curve may have. Once the points are
+    // used up the rest are not read.
     const BEYOND: &str = "pressure strokes beyond the pressure points one document may hold (imported as plain strokes)";
     let ldep = s.obj(ldsc, b"LDeP");
     if ldep.is_some() && r.budget.pressure == 0 {
@@ -377,6 +378,7 @@ pub(crate) fn stroke(r: &mut Reader, pen: ObjId, ldsc: ObjId, local: Affine, beh
             }
         },
         Some(None) => {
+            r.budget.pressure = r.budget.pressure.saturating_sub(crate::geometry::MAX_PRESSURE_CURVE_POINTS);
             r.warn("pressure strokes whose pressure curve can't be read (imported as plain strokes)");
             None
         }
diff --git a/crates/engine/src/cmd/fileio/tests_affinity.rs b/crates/engine/src/cmd/fileio/tests_affinity.rs
index a57da79fc..70b9b992a 100644
--- a/crates/engine/src/cmd/fileio/tests_affinity.rs
+++ b/crates/engine/src/cmd/fileio/tests_affinity.rs
@@ -462,6 +462,12 @@ mod native {
         let flat: Vec<Vec<u8>> = (0..=768).map(|i| node(f64::from(i) / 768.0, 1.0, if i % 3 == 0 { 4 } else { 0 }, (i % 3) as u8)).collect();
         let r = load("flat-many.af", &pressure_documents(flat, 2100)).unwrap();
         assert!(r.warnings.iter().any(|w| w.contains("pressure points one document may hold")), "{:?}", r.warnings);
+
+        // So do curves that can't be read: 768 segments, more than a curve may have.
+        let long: Vec<Vec<u8>> = (0..=768).map(|i| node(f64::from(i) / 768.0, f64::from(i % 2), 4, 0)).collect();
+        let r = load("long-many.af", &pressure_documents(long, 2100)).unwrap();
+        assert!(r.warnings.iter().any(|w| w.contains("pressure curve can't be read")), "{:?}", r.warnings);
+        assert!(r.warnings.iter().any(|w| w.contains("pressure points one document may hold")), "{:?}", r.warnings);
     }
 
     #[test]