diff --git a/crates/compose/src/vars.rs b/crates/compose/src/vars.rs
index b633d7a8f..508ac4a3e 100644
--- a/crates/compose/src/vars.rs
+++ b/crates/compose/src/vars.rs
@@ -66,13 +66,15 @@ struct Hit {
 /// second column comes after its first, however high its entries sit), and stories by where their
 /// first entry on the page is (top to bottom, then left to right).
 fn in_page_order(hits: Vec<Hit>) -> Vec<(usize, String)> {
-    let mut first: HashMap<(usize, StoryId), (i64, i64)> = HashMap::new();
+    // Each story on a page is placed by its first hit there in text order (not its highest hit,
+    // which in a later column could put the whole story ahead of another).
+    let mut first: HashMap<(usize, StoryId), (usize, (i64, i64))> = HashMap::new();
     for h in &hits {
         let (page, y, x) = h.at;
-        first.entry((page, h.story)).and_modify(|f| *f = (*f).min((y, x))).or_insert((y, x));
+        first.entry((page, h.story)).and_modify(|f| *f = (*f).min((h.pos, (y, x)))).or_insert((h.pos, (y, x)));
     }
     let mut hits: Vec<_> =
-        hits.into_iter().map(|h| (h.at.0, first.get(&(h.at.0, h.story)).copied().unwrap_or((h.at.1, h.at.2)), h.story, h.pos, h.text)).collect();
+        hits.into_iter().map(|h| (h.at.0, first.get(&(h.at.0, h.story)).map_or((h.at.1, h.at.2), |f| f.1), h.story, h.pos, h.text)).collect();
     hits.sort_by_key(|a| (a.0, a.1, a.2.0, a.3));
     hits.into_iter().map(|(page, _, _, _, text)| (page, text)).collect()
 }
diff --git a/crates/engine/src/cmd/variables.rs b/crates/engine/src/cmd/variables.rs
index 9c5dd20c8..66cee5fb6 100644
--- a/crates/engine/src/cmd/variables.rs
+++ b/crates/engine/src/cmd/variables.rs
@@ -386,4 +386,41 @@ mod tests {
         assert_eq!(idx.value("Heading", false, designcraft_doc::vars::Use::FirstOnPage, 0), "Alpha");
         assert_eq!(idx.value("Heading", false, designcraft_doc::vars::Use::LastOnPage, 0), "Gamma");
     }
+    /// Stories on one page are ordered by where each one's text starts there: a story whose first
+    /// heading sits low in its first column comes after another story's heading above it, even
+    /// though its later column starts higher still.
+    #[test]
+    fn running_header_orders_stories_by_their_first_heading() {
+        use designcraft_doc::story::COLUMN_BREAK;
+        let mut s = Session::new();
+        s.execute("file.new", &json!({"pages": 1, "facingPages": false})).unwrap();
+        s.execute("style.paragraph.create", &json!({"name": "Heading"})).ok();
+        // Story A, two columns: filler, then Alpha low in column 1; Gamma at the top of column 2.
+        let a_text = format!("{}Alpha{COLUMN_BREAK}\nGamma\ny", "x\n".repeat(8));
+        let a = s.execute("frame.create", &json!({"rect": [72, 72, 300, 400], "content": "text", "text": a_text})).unwrap();
+        s.execute("object.textFrameOptions", &json!({"ids": [a["id"]], "columns": 2, "gutter": 12})).unwrap();
+        // Story B beside it: Beta between Gamma's height and Alpha's.
+        let b_text = "Beta".to_string();
+        let b = s.execute("frame.create", &json!({"rect": [320, 120, 560, 160], "content": "text", "text": b_text})).unwrap();
+        let story =
+            |s: &Session, id: &Value| s.doc().unwrap().doc.item(designcraft_doc::ItemId(id.as_u64().unwrap())).unwrap().text_frame().unwrap().story;
+        let (sa, sb) = (story(&s, &a["id"]), story(&s, &b["id"]));
+        for (sid, text, word) in [(sa, &a_text, "Alpha"), (sa, &a_text, "Gamma"), (sb, &b_text, "Beta")] {
+            let at = text.find(word).unwrap();
+            s.execute("text.select", &json!({"story": sid.0, "anchor": at, "focus": at + word.len()})).unwrap();
+            s.execute("style.paragraph.apply", &json!({"name": "Heading"})).unwrap();
+        }
+        s.execute("variables.define", &json!({"name": "Entry", "type": "runningHeader", "style": "Heading"})).unwrap();
+        let d = s.doc().unwrap().doc.clone();
+        let y = |sid, text: &str, word: &str| {
+            let cs = s.cache.get(&d, sid, None);
+            let (fi, _, b, ..) = crate::compose::caret(&cs, text.find(word).unwrap()).unwrap();
+            d.item(cs.frames[fi].frame).unwrap().bounds().y0 + b
+        };
+        let (ya, yg, yb) = (y(sa, &a_text, "Alpha"), y(sa, &a_text, "Gamma"), y(sb, &b_text, "Beta"));
+        assert!(yg < yb && yb < ya, "Gamma {yg} above Beta {yb} above Alpha {ya}");
+        let idx = s.cache.running_index(&d);
+        assert_eq!(idx.value("Heading", false, designcraft_doc::vars::Use::FirstOnPage, 0), "Beta");
+        assert_eq!(idx.value("Heading", false, designcraft_doc::vars::Use::LastOnPage, 0), "Gamma");
+    }
 }