diff --git a/crates/track/src/face.rs b/crates/track/src/face.rs
index 708a05c4f..7c69c02af 100644
--- a/crates/track/src/face.rs
+++ b/crates/track/src/face.rs
@@ -558,16 +558,19 @@ fn fit_from_face(face: &Face, topo: &Topology, offset: [f64; 2]) -> Option<FaceF
 fn nearest_skin(skin: &[bool], size: (usize, usize), center: (usize, usize), radius: i64) -> Option<(usize, usize)> {
     let (w, h) = size;
     let (ci, cj) = center;
+    // The radius comes from mask geometry: past the window's larger side every ring is outside it.
+    let radius = radius.min(w.max(h) as i64 + 1);
     for r in 0..radius {
         for dj in -r..=r {
-            for di in -r..=r {
-                if di.abs() != r && dj.abs() != r {
-                    continue;
-                }
+            // Only the ring's own pixels: the full rows at the top and bottom, the two ends between.
+            let step = if dj.abs() == r { 1 } else { (2 * r).max(1) };
+            let mut di = -r;
+            while di <= r {
                 let (i, j) = (ci as i64 + di, cj as i64 + dj);
                 if i >= 0 && j >= 0 && (i as usize) < w && (j as usize) < h && skin[j as usize * w + i as usize] {
                     return Some((i as usize, j as usize));
                 }
+                di += step;
             }
         }
     }
@@ -1187,6 +1190,16 @@ pub fn measure(l: &[[f64; 2]; N], reference_height: f64) -> [f64; 14] {
 mod tests {
     use super::*;
 
+    #[test]
+    fn the_skin_search_stays_within_the_window_for_a_huge_radius() {
+        let mut skin = vec![false; 64 * 64];
+        skin[60 * 64 + 5] = true;
+        // A radius from hostile mask geometry costs no more than one that covers the window.
+        assert_eq!(nearest_skin(&skin, (64, 64), (32, 32), i64::MAX), Some((5, 60)));
+        assert_eq!(nearest_skin(&skin, (64, 64), (5, 60), 3), Some((5, 60)));
+        assert_eq!(nearest_skin(&skin, (64, 64), (0, 0), 10), None);
+    }
+
     /// Pearson correlation.
     fn corr(a: &[f64], b: &[f64]) -> f64 {
         let n = a.len() as f64;
diff --git a/crates/track/src/stabilize.rs b/crates/track/src/stabilize.rs
index 092fc4ab4..e8f90f28d 100644
--- a/crates/track/src/stabilize.rs
+++ b/crates/track/src/stabilize.rs
@@ -440,6 +440,12 @@ fn remove_scale(b: &Homography, c: [f64; 2]) -> Homography {
     Homography::scale_about(1.0 / s, p0).then_after(b)
 }
 
+/// Widest window: 3 sigma of the largest Smoothness (1000%) with Smooth More at its maximum, at 240 fps.
+const MAX_SMOOTH_RADIUS: usize = 8640;
+/// Most window taps (frames x radius) one smoothing pass does; past it the window narrows so planning
+/// stays bounded (an hour at 60 fps with the widest setting is about 4.7e8).
+const MAX_SMOOTH_WORK: usize = 1 << 30;
+
 /// Corrective transforms (source → stabilized, before framing) for every frame.
 pub fn corrections(a: &WarpAnalysis, s: &StabSettings) -> Vec<Homography> {
     let n = a.frames.len();
@@ -470,7 +476,8 @@ pub fn corrections(a: &WarpAnalysis, s: &StabSettings) -> Vec<Homography> {
         }
         StabResult::SmoothMotion => {
             let sigma = s.sigma();
-            let rad = ((3.0 * sigma).ceil() as usize).min(n.saturating_sub(1));
+            // 3 sigma covers every supported setting; the work cap only bites on extreme frame counts.
+            let rad = (((3.0 * sigma).ceil() as usize).min(MAX_SMOOTH_RADIUS)).min(n.saturating_sub(1)).min(MAX_SMOOTH_WORK / n);
             for t in 0..n {
                 if sigma < 0.3 || rad == 0 {
                     out.push(Homography::IDENTITY);
@@ -714,6 +721,47 @@ mod tests {
         s / (p.len() - 2) as f64
     }
 
+    #[test]
+    fn a_huge_stored_fps_does_not_widen_the_smoothing_window_past_the_cap() {
+        let (a, _) = shaky(9500);
+        let s = StabSettings { fps: 1e9, preserve_scale: false, ..Default::default() };
+        // Window 8640 each side: one frame is smoothed over at most 17281 frames, not all 9500.
+        let c = corrections(&a, &s);
+        assert_eq!(c.len(), 9500);
+        assert!(c.iter().all(|h| h.0.iter().flatten().all(|v| v.is_finite())));
+        // A jump at frame 9400 is outside frame 0's window (frames 0..=8640): its correction is
+        // unchanged. Smoothing over the whole clip would move it.
+        let (mut jumped, _) = shaky(9500);
+        let f = &mut jumped.frames[9400];
+        f.t[0] += 80.0;
+        f.s[2] += 80.0;
+        f.h[2] += 80.0;
+        let c2 = corrections(&jumped, &s);
+        for (x, y) in c[0].0.iter().flatten().zip(c2[0].0.iter().flatten()) {
+            assert!((x - y).abs() < 1e-9, "{x} vs {y}");
+        }
+        assert!(
+            c[9499].0.iter().flatten().zip(c2[9499].0.iter().flatten()).any(|(x, y)| (x - y).abs() > 1e-6),
+            "the jump does move frames whose window holds it"
+        );
+    }
+
+    #[test]
+    fn the_widest_supported_smoothness_keeps_its_full_window() {
+        // 1000% Smoothness, Smooth More at its maximum, 60 fps: sigma 720 frames, radius 2160.
+        let s = StabSettings { smoothness: 1000.0, crop_less_smooth_more: 100.0, fps: 60.0, preserve_scale: false, ..Default::default() };
+        let (a, _) = shaky(3000);
+        let c = corrections(&a, &s);
+        let (mut jumped, _) = shaky(3000);
+        let f = &mut jumped.frames[2000];
+        f.t[0] += 80.0;
+        f.s[2] += 80.0;
+        f.h[2] += 80.0;
+        let c2 = corrections(&jumped, &s);
+        // Frame 0 sees a jump 2000 frames away (the old 1024-frame cap could not).
+        assert!(c[0].0.iter().flatten().zip(c2[0].0.iter().flatten()).any(|(x, y)| (x - y).abs() > 1e-9));
+    }
+
     #[test]
     fn smoothing_removes_jitter_and_no_motion_locks() {
         let (a, path) = shaky(90);