diff --git a/crates/engine/src/cmd/sketch.rs b/crates/engine/src/cmd/sketch.rs
index 4cf5e4b0..95cf367e 100644
--- a/crates/engine/src/cmd/sketch.rs
+++ b/crates/engine/src/cmd/sketch.rs
@@ -1463,10 +1463,10 @@ pub(super) fn apply_in_order(sk: &mut Sketch, rep: &SolveReport, first: &[Ent],
     if !second_locked {
         ordered(first, second);
     }
-    if !first_locked {
-        for f in first {
-            ordered(&[second], *f);
-        }
+    // Each first entity that can move may (a free symmetry line between two fixed lines, #1796),
+    // even when another of them can't.
+    for f in first.iter().filter(|f| !ent_locked(sk, rep, **f)) {
+        ordered(&[second], *f);
     }
     const TEMP: &str = "__keep_size";
     for (h, extra) in tries {
diff --git a/crates/engine/src/cmd/sketch_constraints_tests.rs b/crates/engine/src/cmd/sketch_constraints_tests.rs
index 4e3efc03..c68343ff 100644
--- a/crates/engine/src/cmd/sketch_constraints_tests.rs
+++ b/crates/engine/src/cmd/sketch_constraints_tests.rs
@@ -283,3 +283,23 @@ fn an_angle_between_lines_takes_the_reading_nearest_its_value_and_reports_degree
     let d = run(&mut s, "sketch.dimension", json!({"entities": ["l2"], "driven": true}));
     assert_eq!(d["unit"], "mm", "{d}");
 }
+
+#[test]
+fn symmetry_moves_a_free_line_between_two_fixed_lines() {
+    // #1796: with both mirrored lines fixed, the symmetry line between them (a free construction
+    // line) is the one to move; it was refused as "neither entity can move".
+    let mut s = new_sketch();
+    run(&mut s, "sketch.line", json!({"points": [[0, 0], [0, 20]], "ids": ["left"]}));
+    run(&mut s, "sketch.line", json!({"points": [[10, 0], [10, 20]], "ids": ["right"]}));
+    run(&mut s, "sketch.line", json!({"points": [[3, 0], [3, 20]], "construction": true, "ids": ["mid"]}));
+    run(&mut s, "sketch.constraint.fix", json!({"entities": ["left", "right"]}));
+    run(&mut s, "sketch.constraint.symmetry", json!({"a": "left", "b": "right", "line": "mid"}));
+    let sk = sketch(&s);
+    let at = |r: &str| sk.point(sk.resolve_point(r).unwrap()).unwrap();
+    for end in ["mid.start", "mid.end"] {
+        assert!((at(end).x - 5.0).abs() < 1e-7, "{end} at {:?}", at(end));
+    }
+    for (end, x) in [("left.start", 0.0), ("left.end", 0.0), ("right.start", 10.0), ("right.end", 10.0)] {
+        assert!((at(end).x - x).abs() < 1e-9, "{end} moved to {:?}", at(end));
+    }
+}