diff --git a/crates/doc/src/appearance.rs b/crates/doc/src/appearance.rs
index cfb4eb10..13821e01 100644
--- a/crates/doc/src/appearance.rs
+++ b/crates/doc/src/appearance.rs
@@ -239,6 +239,12 @@ impl Document {
 
 /// The B-rep face of a body nearest a point (within 5% of the body's size).
 pub fn face_index_at(b: &crate::ModelBody, p: Vec3) -> Option<usize> {
+    let (d, f) = nearest_face(b, p)?;
+    (d <= pick_tolerance(b)).then_some(f)
+}
+
+/// The face of `b` nearest `p` and how far it is, however far.
+pub fn nearest_face(b: &crate::ModelBody, p: Vec3) -> Option<(f64, usize)> {
     let m = b.mesh();
     let mut best: Option<(f64, u32)> = None;
     for (t, f) in m.triangles.iter().zip(&m.tri_face) {
@@ -248,8 +254,12 @@ pub fn face_index_at(b: &crate::ModelBody, p: Vec3) -> Option<usize> {
             best = Some((d, *f));
         }
     }
-    let (d, f) = best?;
-    (d <= b.body.size() * 0.05 + 1e-6).then_some(f as usize)
+    best.map(|(d, f)| (d, f as usize))
+}
+
+/// How far from a face of `b` a picked point may lie and still pick it (`face_index_at`).
+pub fn pick_tolerance(b: &crate::ModelBody) -> f64 {
+    b.body.size() * 0.05 + 1e-6
 }
 
 /// The point of triangle abc nearest p.
diff --git a/crates/doc/src/eval.rs b/crates/doc/src/eval.rs
index 3b5cb980..5f361a8f 100644
--- a/crates/doc/src/eval.rs
+++ b/crates/doc/src/eval.rs
@@ -2901,52 +2901,62 @@ mod surface;
 pub fn object_height(st: &ModelState, plane: &Plane, centre: Vec3, p: Vec3) -> f64 {
     let n = plane.normal();
     let h = |q: Vec3| (q - plane.origin).dot(n);
-    for b in st.bodies.iter().filter(|b| !b.body.is_mesh()) {
-        let tol = (b.body.size() * 1e-3).max(1e-3);
-        let Ok(faces) = b.body.faces(tol) else { continue };
-        let m = b.mesh();
-        let on: Vec<usize> = faces.iter().filter(|f| crate::appearance::face_index_at(b, p) == Some(f.index)).map(|f| f.index).collect();
-        let Some(&fi) = on.first() else { continue };
-        if let Some(f) = faces.iter().find(|f| f.index == fi)
-            && f.plane_normal.is_some_and(|fnrm| fnrm.cross(n).len() < 1e-6)
+    let Some((bi, fi)) = face_at(st, p) else { return h(p) };
+    let Some(b) = st.bodies.get(bi) else { return h(p) };
+    let tol = (b.body.size() * 1e-3).max(1e-3);
+    let Ok(faces) = b.body.faces(tol) else { return h(p) };
+    if let Some(f) = faces.iter().find(|f| f.index == fi)
+        && f.plane_normal.is_some_and(|fnrm| fnrm.cross(n).len() < 1e-6)
+    {
+        return h(f.centroid);
+    }
+    // A curved or slanted face: where the profile's middle meets it.
+    let m = b.mesh();
+    for dir in [n, n * -1.0] {
+        if let Some((t, tri)) = m.raycast(centre, dir)
+            && m.tri_face.get(tri).is_some_and(|x| *x as usize == fi)
         {
-            return h(f.centroid);
+            return h(centre + dir * t);
         }
-        // A curved or slanted face: where the profile's middle meets it.
-        for dir in [n, n * -1.0] {
-            if let Some((t, tri)) = m.raycast(centre, dir)
-                && m.tri_face.get(tri).is_some_and(|x| *x as usize == fi)
-            {
-                return h(centre + dir * t);
-            }
-        }
-        return h(p);
     }
     h(p)
 }
 
+/// The face a To Object pick is on: the nearest face over every solid body, `(body index,
+/// face index)`, within that body's pick tolerance. Not the first body with any face within
+/// its tolerance: that is 5 % of the body's size, so a large body beside a small target (a
+/// plate under a post, a frame around a pin) would otherwise take a pick made on the target.
+fn face_at(st: &ModelState, p: Vec3) -> Option<(usize, usize)> {
+    st.bodies
+        .iter()
+        .enumerate()
+        .filter(|(_, b)| !b.body.is_mesh())
+        .filter_map(|(bi, b)| {
+            let (d, fi) = crate::appearance::nearest_face(b, p)?;
+            (d <= crate::appearance::pick_tolerance(b)).then_some((d, bi, fi))
+        })
+        .min_by(|a, b| a.0.total_cmp(&b.0))
+        .map(|(_, bi, fi)| (bi, fi))
+}
+
 /// The body at `p` when the face there is not a plane square to `n` (To Object must then
 /// follow the face's shape).
 fn curved_target(st: &ModelState, n: Vec3, p: Vec3) -> Option<usize> {
-    for (bi, b) in st.bodies.iter().enumerate().filter(|(_, b)| !b.body.is_mesh()) {
-        let Some(fi) = crate::appearance::face_index_at(b, p) else { continue };
-        let tol = (b.body.size() * 1e-3).max(1e-3);
-        let planar =
-            b.body.faces(tol).ok()?.into_iter().find(|f| f.index == fi).and_then(|f| f.plane_normal).is_some_and(|fnrm| fnrm.cross(n).len() < 1e-6);
-        return (!planar).then_some(bi);
-    }
-    None
+    let (bi, fi) = face_at(st, p)?;
+    let b = st.bodies.get(bi)?;
+    let tol = (b.body.size() * 1e-3).max(1e-3);
+    let planar =
+        b.body.faces(tol).ok()?.into_iter().find(|f| f.index == fi).and_then(|f| f.plane_normal).is_some_and(|fnrm| fnrm.cross(n).len() < 1e-6);
+    (!planar).then_some(bi)
 }
 
 /// The body at `p` when the face there is not planar.
 fn curved_target_any(st: &ModelState, p: Vec3) -> Option<usize> {
-    for (bi, b) in st.bodies.iter().enumerate().filter(|(_, b)| !b.body.is_mesh()) {
-        let Some(fi) = crate::appearance::face_index_at(b, p) else { continue };
-        let tol = (b.body.size() * 1e-3).max(1e-3);
-        let planar = b.body.faces(tol).ok()?.into_iter().find(|f| f.index == fi).is_some_and(|f| f.plane_normal.is_some());
-        return (!planar).then_some(bi);
-    }
-    None
+    let (bi, fi) = face_at(st, p)?;
+    let b = st.bodies.get(bi)?;
+    let tol = (b.body.size() * 1e-3).max(1e-3);
+    let planar = b.body.faces(tol).ok()?.into_iter().find(|f| f.index == fi).is_some_and(|f| f.plane_normal.is_some());
+    (!planar).then_some(bi)
 }
 
 /// Tools run through `target`, cut back to its surface: each tool less the body, keeping the
diff --git a/crates/engine/src/extent_tests.rs b/crates/engine/src/extent_tests.rs
index 1396c6a3..961beccc 100644
--- a/crates/engine/src/extent_tests.rs
+++ b/crates/engine/src/extent_tests.rs
@@ -104,3 +104,24 @@ fn revolve_to_a_cylinder_follows_it() {
     }
     panic!("neither post was reached");
 }
+
+/// To Object picks the face that is at the picked point, not the first body with any face
+/// near it. Here the pick is on a post (r 2.75) only 2 mm above a plate: the ridge must end
+/// on the post. Before, the plate (within 5 % of its size of the pick) was taken as the
+/// target, nothing trimmed the tool, and the ridge ran past the post.
+#[test]
+fn extrude_to_a_cylinder_beside_another_body() {
+    let mut s = Session::default();
+    run(&mut s, "solid.box", json!({"corner": [-98, -5, 0], "length": 101, "width": 10, "height": 3, "body_name": "Plate"}));
+    run(&mut s, "solid.cylinder", json!({"base": [0, 0, 0], "axis": [0, 0, 1], "radius": 2.75, "height": 10, "body_name": "Post"}));
+    // A ridge above the plate, y -1.5..0, z 4..7, from the plate's far end towards the post.
+    run(&mut s, "sketch.create", json!({"plane": {"origin": [-98, 0, 0], "x_dir": [0, 1, 0], "y_dir": [0, 0, 1]}, "name": "End"}));
+    run(&mut s, "sketch.rectangle.two_point", json!({"p0": [-1.5, 4], "p1": [0, 7]}));
+    run(&mut s, "sketch.finish", json!({}));
+    run(&mut s, "solid.extrude", json!({"sketch": "End", "to": [-2.75, 0, 5], "operation": "new", "body_name": "Ridge"}));
+    let b = body(&mut s, "Ridge");
+    // Its end follows the post: farthest at the ridge's edge y = -1.5, x = -√(2.75² − 1.5²).
+    let end = b["bbox"]["max"][0].as_f64().unwrap_or(f64::MAX);
+    assert!((end + (2.75f64 * 2.75 - 1.5 * 1.5).sqrt()).abs() < 1e-3, "{b}");
+    assert!((b["bbox"]["min"][0].as_f64().unwrap_or(0.0) + 98.0).abs() < 1e-6, "{b}");
+}