diff --git a/crates/render/src/dots.rs b/crates/render/src/dots.rs
index b13cbdd57..f3effd1f1 100644
--- a/crates/render/src/dots.rs
+++ b/crates/render/src/dots.rs
@@ -57,7 +57,7 @@ pub(crate) fn draw(pix: &mut Pixmap, view: &View, d: &Dots) {
     let strong = |k: i64| k.rem_euclid(major) == 0;
     // The device-pixel span of the mark on line `k` along an axis `len` pixels long from `o`.
     let span = |k: i64, o: f64, len: i64| {
-        let a = ((k as f64 * d.step * s - o).round() as i64).saturating_sub(lead);
+        let a = (nearest_px(k as f64 * d.step * s - o) as i64).saturating_sub(lead);
         (a.max(0), a.saturating_add(side).min(len))
     };
     let row = w as usize * 4;
@@ -92,6 +92,15 @@ pub(crate) fn draw(pix: &mut Pixmap, view: &View, d: &Dots) {
     }
 }
 
+/// The device pixel nearest `p` pixels from the view's top-left. A mark halfway between two pixels
+/// goes to the right (or lower) one on either side of the origin, and `p` is first rounded to
+/// 1/65536 px: a view a whole number of pixels off (a pan, a band, a patch) reaches it with another
+/// rounding error, and would otherwise put the marks that fall halfway on the other pixel.
+fn nearest_px(p: f64) -> f64 {
+    const STEPS: f64 = 65_536.0;
+    ((p * STEPS).round() / STEPS + 0.5).floor()
+}
+
 /// Which line covers each device pixel along an axis: 0 none, 1 a faded one, 2 a strong one.
 type Cover = Vec<u8>;
 
diff --git a/crates/render/src/dots_tests.rs b/crates/render/src/dots_tests.rs
index 53d052062..a5ff2edc9 100644
--- a/crates/render/src/dots_tests.rs
+++ b/crates/render/src/dots_tests.rs
@@ -134,3 +134,27 @@ fn graph_paper_is_strong_every_major_line() {
         assert_eq!(at(x, -195), strong, "a strong line at {x}");
     }
 }
+
+/// At a zoom of 1.0625, a step of 24 is 25.5 pixels: every second dot falls halfway between two
+/// pixels. A view a whole number of pixels on (a pan, a band, a patch) has to put it on the same
+/// one, on whichever side of that view's origin it is.
+#[test]
+fn dots_halfway_between_pixels_stay_put() {
+    let (d, page) = page_with_square();
+    for lines in [false, true] {
+        let opts = Options { dots: Some(Dots { lines, ..dots() }), ..Default::default() };
+        let s = 1.0625;
+        let full = View { origin: (0.0, 0.0), scale: s, width: 400, height: 300 };
+        let a = render_view_single(&d, page, &full, &opts).unwrap();
+        for dx in 1..100u32 {
+            let dy = (dx * 37) % 100;
+            let v = View { origin: (f64::from(dx) / s, f64::from(dy) / s), scale: s, width: 250, height: 180 };
+            let b = render_view_single(&d, page, &v, &opts).unwrap();
+            for y in 0..180 {
+                for x in 0..250 {
+                    assert_eq!(rgba(&b, x, y), rgba(&a, x + dx, y + dy), "lines {lines}, a pan by ({dx}, {dy}), at {x}, {y}");
+                }
+            }
+        }
+    }
+}