diff --git a/src/app/command_driver.rs b/src/app/command_driver.rs
index d8a2f787a..65385f215 100644
--- a/src/app/command_driver.rs
+++ b/src/app/command_driver.rs
@@ -3486,6 +3486,53 @@ impl OpenCADStudio {
                         }
                     }
                 }
+                // The solver cannot start from an axis lying exactly across
+                // the datum (its equations are singular there), so turn the
+                // object onto the axis about its anchor first — the
+                // reference turns it about that anchor too — and let the
+                // constraint hold what already fits.
+                if let Some((handle, anchor, end, vertex)) =
+                    crate::scene::parametric_constraints::axis_alignment_target(
+                        &self.tabs[i].scene.document,
+                        &refs,
+                    )
+                {
+                    let axis = (end.x - anchor.x, end.y - anchor.y);
+                    let length = axis.0.hypot(axis.1);
+                    let target = if axis.0 * direction.x + axis.1 * direction.y >= 0.0 {
+                        (direction.x, direction.y)
+                    } else {
+                        (-direction.x, -direction.y)
+                    };
+                    let angle = (axis.0 * target.1 - axis.1 * target.0)
+                        .atan2(axis.0 * target.0 + axis.1 * target.1);
+                    if length > 1.0e-9 && angle.abs() > 1.0e-9 {
+                        match vertex {
+                            Some(index) => {
+                                let moved =
+                                    self.tabs[i].scene.document.get_entity(handle).cloned();
+                                if let Some(mut entity) = moved {
+                                    if crate::scene::parametric_constraints::set_polyline_vertex(
+                                        &mut entity,
+                                        index,
+                                        anchor.x + length * target.0,
+                                        anchor.y + length * target.1,
+                                    ) {
+                                        self.tabs[i].scene.update_entity(entity);
+                                    }
+                                }
+                            }
+                            None => self.tabs[i].scene.transform_entities(
+                                &[handle],
+                                &EntityTransform::Rotate {
+                                    center: glam::DVec3::new(anchor.x, anchor.y, anchor.z),
+                                    axis: glam::DVec3::Z,
+                                    angle_rad: angle,
+                                },
+                            ),
+                        }
+                    }
+                }
                 let id = self.tabs[i]
                     .scene
                     .parametric_constraint_set_mut(scope)
diff --git a/src/scene/parametric_constraints.rs b/src/scene/parametric_constraints.rs
index e599ceb4f..bd0ee0c99 100644
--- a/src/scene/parametric_constraints.rs
+++ b/src/scene/parametric_constraints.rs
@@ -202,6 +202,69 @@ pub(crate) fn directional_axis_endpoints(
     }
 }
 
+/// The axis a lone Horizontal/Vertical reference — or two points on one
+/// entity — turns onto its datum: the entity, the anchor that stays, the
+/// axis end that moves, and for a polyline the vertex to move instead of
+/// turning the whole entity.
+pub(crate) fn axis_alignment_target(
+    document: &acadrust::CadDocument,
+    refs: &[ParametricRef],
+) -> Option<(Handle, Vector3, Vector3, Option<usize>)> {
+    let (handle, start_marker, end_marker) = match refs {
+        [reference] => {
+            let entity = document.get_entity(reference.entity)?;
+            if reference.directional_axis().is_some() {
+                let [start, end] = directional_axis_endpoints(entity, *reference)?;
+                return Some((reference.entity, start, end, None));
+            }
+            let index = reference.segment_index().map_or(0, |index| index as i32);
+            (reference.entity, index, index + 1)
+        }
+        [first, second] if first.entity == second.entity => {
+            (first.entity, first.marker?, second.marker?)
+        }
+        _ => return None,
+    };
+    let entity = document.get_entity(handle)?;
+    let start = resolve_point(entity, start_marker)?;
+    let end = resolve_point(entity, end_marker)?;
+    let vertex = matches!(
+        entity,
+        acadrust::EntityType::LwPolyline(_) | acadrust::EntityType::Polyline2D(_)
+    )
+    .then(|| usize::try_from(end_marker).ok())
+    .flatten();
+    Some((handle, start, end, vertex))
+}
+
+/// Moves one polyline vertex in its plane; `false` for any other entity.
+pub(crate) fn set_polyline_vertex(
+    entity: &mut acadrust::EntityType,
+    index: usize,
+    x: f64,
+    y: f64,
+) -> bool {
+    match entity {
+        acadrust::EntityType::LwPolyline(polyline) => polyline
+            .vertices
+            .get_mut(index)
+            .map(|vertex| {
+                vertex.location.x = x;
+                vertex.location.y = y;
+            })
+            .is_some(),
+        acadrust::EntityType::Polyline2D(polyline) => polyline
+            .vertices
+            .get_mut(index)
+            .map(|vertex| {
+                vertex.location.x = x;
+                vertex.location.y = y;
+            })
+            .is_some(),
+        _ => false,
+    }
+}
+
 /// Grabbed points are exact kernel inputs; the solver anchors the remaining
 /// endpoint coordinates according to the line's directional constraints.
 pub(crate) fn grip_solve_anchor_refs(