diff --git a/crates/engine/src/cmd/contact_sweep.rs b/crates/engine/src/cmd/contact_sweep.rs
index 3f5a3483..539fc6a0 100644
--- a/crates/engine/src/cmd/contact_sweep.rs
+++ b/crates/engine/src/cmd/contact_sweep.rs
@@ -162,7 +162,7 @@ impl ContactGeometry {
 
     /// How many pairs of set members are checked against each other.
     pub(super) fn pair_count(&self) -> usize {
-        self.pairs.iter().map(|(_, _, a, b)| (a.0, b.0)).collect::<BTreeSet<_>>().len()
+        self.pairs.iter().map(|(_, _, a, b)| (a.0.min(b.0), a.0.max(b.0))).collect::<BTreeSet<_>>().len()
     }
 
     fn frame(body: &CachedBody, s: &Session) -> Result<Mat> {
diff --git a/crates/ui-egui/src/dialogs_motion.rs b/crates/ui-egui/src/dialogs_motion.rs
index 7dc65ac0..809b35ab 100644
--- a/crates/ui-egui/src/dialogs_motion.rs
+++ b/crates/ui-egui/src/dialogs_motion.rs
@@ -203,18 +203,17 @@ fn transport(ui: &mut egui::Ui, what: Transport, tip: &str) -> egui::Response {
     resp.on_hover_text(tip)
 }
 
-/// Study `key` (an id or a name) as the Motion Study dialog edits it: (id, name, steps, keys as
-/// tracks with values in degrees and mm). The dialog keys whole steps, so a study keyed between
-/// them (made by a command) is refused rather than rounded.
-pub fn study_tracks(s: &Session, key: &str) -> Result<(u64, String, String, Vec<Track>), String> {
+/// Study `key` as the Motion Study dialog edits it: (id, name, steps, keys as tracks with values
+/// in degrees and mm). `key` is an id first when `id_first`, else a name first (as
+/// `motion.study` reads a number and text). The dialog keys whole steps of its timeline, so a
+/// study keyed between them or off it (made by a command) is refused rather than changed.
+pub fn study_tracks(s: &Session, key: &str, id_first: bool) -> Result<(u64, String, String, Vec<Track>), String> {
     let studies = &s.doc.assembly.studies;
-    let m = studies
-        .iter()
-        .find(|m| m.id.to_string() == key)
-        .or_else(|| studies.iter().find(|m| m.name == key))
-        .ok_or_else(|| format!("no motion study `{key}`"))?;
-    if m.keys.iter().flat_map(|k| &k.points).any(|(st, _)| st.fract() != 0.0) {
-        return Err(format!("{} has keys between whole steps, which this dialog can't keep: edit it with motion.study", m.name));
+    let (by_id, by_name) = (studies.iter().find(|m| m.id.to_string() == key), studies.iter().find(|m| m.name == key));
+    let m = if id_first { by_id.or(by_name) } else { by_name.or(by_id) }.ok_or_else(|| format!("no motion study `{key}`"))?;
+    let last = f64::from(m.steps);
+    if m.keys.iter().flat_map(|k| &k.points).any(|(st, _)| st.fract() != 0.0 || !(0.0..=last).contains(st)) {
+        return Err(format!("{} has keys between whole steps or off its timeline, which this dialog can't keep: edit it with motion.study", m.name));
     }
     let tracks = m
         .keys
@@ -238,13 +237,13 @@ pub fn preset(s: &Session, k: &mut Mo, p: &Value) -> Result<(), String> {
     if let Some(key) = o.keys().find(|k| k.as_str() != "study") {
         return Err(format!("unknown param `{key}` (Motion Study takes study)"));
     }
-    let key = match o.get("study") {
-        Some(Value::Number(n)) => n.to_string(),
-        Some(Value::String(x)) => x.clone(),
+    let (key, id_first) = match o.get("study") {
+        Some(Value::Number(n)) => (n.to_string(), true),
+        Some(Value::String(x)) => (x.clone(), false),
         Some(_) => return Err("`study` must be an id or a name".into()),
         None => return Ok(()),
     };
-    let (id, n, st, t) = study_tracks(s, &key)?;
+    let (id, n, st, t) = study_tracks(s, &key, id_first)?;
     (*study, *name, *steps, *tracks, *shown) = (Some(id.to_string()), n, st, t, None);
     Ok(())
 }
@@ -506,7 +505,7 @@ pub fn rows(app: &mut SolveApp, ui: &mut egui::Ui, k: &mut Mo, inputs: &mut [Sel
                 combo(ui, "ms_study", &labels, &mut pick);
                 ui.end_row();
                 if pick != was {
-                    match pick.checked_sub(1).and_then(|i| studies.get(i)).map(|(id, _)| study_tracks(&app.session, id)) {
+                    match pick.checked_sub(1).and_then(|i| studies.get(i)).map(|(id, _)| study_tracks(&app.session, id, true)) {
                         Some(Ok((id, n, st, t))) => {
                             (*study, *name, *steps, *tracks, *shown, *playing) = (Some(id.to_string()), n, st, t, None, false)
                         }
diff --git a/crates/ui-egui/src/dialogs_motion_plot.rs b/crates/ui-egui/src/dialogs_motion_plot.rs
index 49aa0d0b..52515f47 100644
--- a/crates/ui-egui/src/dialogs_motion_plot.rs
+++ b/crates/ui-egui/src/dialogs_motion_plot.rs
@@ -461,9 +461,12 @@ mod tests {
             .run("motion.study", json!({"name": "Push", "steps": 15, "keys": [{"joint": "Rail", "points": [[0, 10], [15, -5]]}]}))
             .unwrap()["study"]
             .to_string();
-        // A study keyed between whole steps is not opened (the dialog would round its keys).
+        // A study keyed between whole steps or off its timeline is not opened (the dialog would move its keys).
         h.app.run("motion.study", json!({"name": "Fine", "steps": 15, "keys": [{"joint": "Rail", "points": [[0, 10], [7.5, -5]]}]})).unwrap();
-        for bad in [json!({"study": "Nope"}), json!({"study": "Push", "step": 3}), json!({"study": [1]}), json!({"study": "Fine"})] {
+        h.app.run("motion.study", json!({"name": "Off", "steps": 15, "keys": [{"joint": "Rail", "points": [[-1, 10], [15, -5]]}]})).unwrap();
+        for bad in
+            [json!({"study": "Nope"}), json!({"study": "Push", "step": 3}), json!({"study": [1]}), json!({"study": "Fine"}), json!({"study": "Off"})]
+        {
             let r = h.call("ui.start", json!({"command": "motion.study", "params": bad}));
             assert!(r["ok"] == false && h.app.dialog.is_none(), "{bad}: {r}");
         }
diff --git a/docs/book/src/guide/assemblies.md b/docs/book/src/guide/assemblies.md
index fa354800..311545ff 100644
--- a/docs/book/src/guide/assemblies.md
+++ b/docs/book/src/guide/assemblies.md
@@ -193,10 +193,11 @@ colliding pair with its `first_step`, `last_step`, the `steps` ranges where they
 far into each other (`depth_mm`, the most at `deepest_step`) and their shared `volume_mm3`
 there (null when it is not cheap to work out). It plays the study as `motion.play` does, but
 contact sets don't stop it, and parts are tested at the samples only: a part that passes right
-through another between two samples is missed. A check
-takes at most 256 bodies; on a large design, list the `occurrences` to check (an arm, with
-`against` the parts it must miss). When the work runs out it says `truncated` and the step it
-`checked_to`.
+through another between two samples is missed. Parts are told apart by occurrence, as contact
+sets tell them apart: an occurrence inside a sub-assembly placed twice is one part, so its two
+copies are not checked against each other. A check takes at most 256 bodies; on a large design,
+list the `occurrences` to check (an arm, with `against` the parts it must miss). When the work
+runs out it says `truncated` and the step it `checked_to`.
 
 **Insert Design** (`component.insert_design {path, translate?}`, on the **ASSEMBLE** panel and
 in the **File** menu) adds a component linked to another saved design, so each part can live in