diff --git a/crates/engine/src/library.rs b/crates/engine/src/library.rs
index 936d798a..df67c571 100644
--- a/crates/engine/src/library.rs
+++ b/crates/engine/src/library.rs
@@ -582,11 +582,15 @@ fn local_key(lid: &str, key: &str, taken: impl Fn(&str) -> bool) -> String {
 }
 
 /// Copy library styles `keys` into `doc` as linked remote styles (with `update`, copies older than
-/// the library's are refreshed). Returns library style id → local id.
+/// the library's are refreshed). The variables a written copy binds are imported too and its
+/// bindings point at their copies (never at this file's variables of the same ids). Returns library
+/// style id → local id.
 pub fn import_styles(doc: &mut Document, lib: &PublishedLibrary, keys: &BTreeSet<String>, update: bool) -> BTreeMap<String, String> {
     let lid = lib.manifest.id.clone();
     let mut out = BTreeMap::new();
     let mut hashes = BTreeSet::new();
+    // Local ids of the copies written now, with the library style they copy.
+    let mut written: Vec<(String, &Style)> = Vec::new();
     for key in keys {
         let Some(style) = lib.doc.styles.iter().find(|s| s.id == *key) else { continue };
         let version = lib.manifest.style(key).map_or(lib.manifest.version, |s| s.version);
@@ -598,6 +602,7 @@ pub fn import_styles(doc: &mut Document, lib: &PublishedLibrary, keys: &BTreeSet
                 {
                     *slot = Style { id: r.local.clone(), ..style.clone() };
                     set_record(&mut doc.libraries_mut().styles, ImportedStyle { version, ..r.clone() });
+                    written.push((r.local.clone(), style));
                 }
                 r.local
             }
@@ -605,6 +610,7 @@ pub fn import_styles(doc: &mut Document, lib: &PublishedLibrary, keys: &BTreeSet
                 let local = local_key(&lid, key, |l| doc.styles.iter().any(|s| s.id == l));
                 doc.styles.push(Style { id: local.clone(), ..style.clone() });
                 set_record(&mut doc.libraries_mut().styles, ImportedStyle { library: lid.clone(), key: key.clone(), local: local.clone(), version });
+                written.push((local.clone(), style));
                 local
             }
         };
@@ -613,6 +619,17 @@ pub fn import_styles(doc: &mut Document, lib: &PublishedLibrary, keys: &BTreeSet
         }
         out.insert(key.clone(), local);
     }
+    let bound: BTreeSet<VariableId> = written.iter().flat_map(|(_, s)| s.bound.values().cloned()).collect();
+    if !bound.is_empty() {
+        let vars = import_variables(doc, lib, &bound, &BTreeSet::new(), update);
+        for (local, _) in &written {
+            if let Some(slot) = doc.styles.iter_mut().find(|s| s.id == *local) {
+                // Bindings to variables the library lacks are dropped (the published value stays).
+                slot.bound =
+                    std::mem::take(&mut slot.bound).into_iter().filter_map(|(f, v)| vars.variables.get(&v).map(|l| (f, l.clone()))).collect();
+            }
+        }
+    }
     copy_images(doc, &lib.doc, &hashes);
     out
 }
diff --git a/crates/engine/src/library_variables_tests.rs b/crates/engine/src/library_variables_tests.rs
index 4bbaad57..4fc778a7 100644
--- a/crates/engine/src/library_variables_tests.rs
+++ b/crates/engine/src/library_variables_tests.rs
@@ -314,3 +314,33 @@ fn library_variable_commands_fail_cleanly() {
     }
     assert!(s.doc().unwrap().libraries.is_empty());
 }
+
+#[test]
+fn library_style_bindings_ignore_unrelated_local_variables() {
+    let d = dir("style-bound");
+    let path = path_str(&d.join("lib.figcraft"));
+    let mut lib = Session::new();
+    ex(&mut lib, "variable.createCollection", json!({"name": "Tokens"}));
+    let var = ex(&mut lib, "variable.create", json!({"collection": "Tokens", "name": "Brand", "type": "color", "value": "#0000ff"}))["id"].clone();
+    let style = ex(&mut lib, "style.create", json!({"type": "paint", "name": "Brand", "value": "#0000ff"}))["id"].clone();
+    ex(&mut lib, "style.bind", json!({"style": style, "field": "fill", "variable": var}));
+    let lid = publish_to(&mut lib, &path);
+
+    let mut s = Session::new();
+    ex(&mut s, "variable.createCollection", json!({"name": "Local"}));
+    let local = ex(&mut s, "variable.create", json!({"collection": "Local", "name": "Unrelated", "type": "color", "value": "#ff0000"}))["id"].clone();
+    assert_eq!(local, var, "the ids must collide for this test");
+    let r = idv(&ex(&mut s, "shape.rectangle", json!({"width": 40, "height": 40})));
+    ex(&mut s, "library.add", json!({"path": path}));
+    ex(&mut s, "library.applyStyle", json!({"library": lid, "style": "Brand", "id": r}));
+    assert_eq!(fill(&s, r), "0000FF");
+    healthy(&s);
+
+    // An updated style follows the library's variable, not the local one.
+    ex(&mut lib, "variable.set", json!({"variable": "Brand", "value": "#00ffff"}));
+    republish(&mut lib);
+    ex(&mut s, "library.acceptUpdates", json!({}));
+    assert_eq!(fill(&s, r), "00FFFF");
+    healthy(&s);
+    let _ = std::fs::remove_dir_all(&d);
+}