diff --git a/crates/compose/src/lib.rs b/crates/compose/src/lib.rs
index 3dd7c25b3..56f21361d 100644
--- a/crates/compose/src/lib.rs
+++ b/crates/compose/src/lib.rs
@@ -2018,10 +2018,20 @@ fn cjk_em_box(g: &Glyph) -> (f64, f64) {
     let top = -height * g.ascent / (g.ascent + g.descent).max(1e-9);
     (top, top + height)
 }
+/// Em box that character alignment lines up, relative to the baseline (y down) at the glyph's
+/// size: the font's `BASE` em box, else 0.88 em above and 0.12 em below the baseline. A font's
+/// ascender/descender proportions put a Latin em box's centre too low for this.
+fn alignment_em_box(g: &Glyph) -> (f64, f64) {
+    let upem = g.face.units_per_em();
+    let (top, bottom) = g.face.base_em_box().unwrap_or((upem * 0.88, upem * -0.12));
+    let k = g.sy.abs();
+    (-top * k, -bottom * k)
+}
+/// Upward shift that puts `g`'s em box (or ICF) edge or centre where the reference glyph's is.
 fn cjk_alignment_shift(g: &Glyph, reference: &Glyph) -> f64 {
     use designcraft_doc::cjk::CharacterAlignment as A;
-    let (t, b) = cjk_em_box(g);
-    let (rt, rb) = cjk_em_box(reference);
+    let (t, b) = alignment_em_box(g);
+    let (rt, rb) = alignment_em_box(reference);
     match g.character_alignment {
         A::Baseline => 0.0,
         A::EmTop => t - rt,
diff --git a/crates/compose/src/tests.rs b/crates/compose/src/tests.rs
index 0d1fe2d27..7f3630d54 100644
--- a/crates/compose/src/tests.rs
+++ b/crates/compose/src/tests.rs
@@ -1490,17 +1490,39 @@ fn cjk_center_leading_measures_em_centers_across_different_sizes() {
 }
 
 #[test]
-fn cjk_em_center_alignment_moves_small_characters() {
-    let (mut d, sid, _) = doc_with("AB", Rect::new(0.0, 0.0, 300.0, 100.0), ParaAttrs::default());
-    d.story_mut(sid).unwrap().format_chars(0..1, |f| f.over.size = Some(24.0));
-    d.story_mut(sid).unwrap().format_chars(1..2, |f| f.over.character_alignment = Some(designcraft_doc::cjk::CharacterAlignment::EmCenter));
-    let cs = compose_story(&d, sid, &ComposeOptions::default());
-    let line = &cs.frames[0].lines[0];
-    let center = |g: &PlacedGlyph| {
-        let (a, b) = g.face.vertical_metrics();
-        g.y + (b - a) / (2.0 * (a + b)) * g.face.units_per_em() * g.sy
+fn smaller_cjk_run_aligns_to_the_line_em_box_centre() {
+    use designcraft_doc::cjk::CharacterAlignment;
+    let text = "Ab 甲乙 cd";
+    let run = "Ab ".len().."Ab 甲乙".len();
+    // Em box centre (y down) of a placed glyph: its font's BASE em box, else 0.88/-0.12 em.
+    let centre = |l: &Line, g: &PlacedGlyph| {
+        let upem = g.face.units_per_em();
+        let (top, bottom) = g.face.base_em_box().unwrap_or((upem * 0.88, upem * -0.12));
+        l.baseline + g.y - (top + bottom) / 2.0 * g.sy
     };
-    assert!((center(&line.glyphs[0]) - center(&line.glyphs[1])).abs() < 1e-6);
+    for alignment in [CharacterAlignment::EmCenter, CharacterAlignment::Baseline] {
+        let (mut d, sid, _) = doc_with(text, Rect::new(0.0, 0.0, 300.0, 100.0), ParaAttrs::default());
+        d.story_mut(sid).unwrap().format_chars(0..text.len(), |f| {
+            f.over.size = Some(10.0);
+            f.over.character_alignment = Some(alignment);
+        });
+        d.story_mut(sid).unwrap().format_chars(run.clone(), |f| f.over.size = Some(6.0));
+        let cs = compose_story(&d, sid, &ComposeOptions::default());
+        let line = &cs.frames[0].lines[0];
+        let latin = &line.glyphs[0];
+        let cjk: Vec<&PlacedGlyph> = line.glyphs.iter().filter(|g| run.contains(&g.byte)).collect();
+        assert_eq!(cjk.len(), 2);
+        assert!(latin.y.abs() < 1e-9);
+        for g in cjk {
+            match alignment {
+                CharacterAlignment::EmCenter => {
+                    assert!((centre(line, g) - centre(line, latin)).abs() < 0.01, "{} vs {}", centre(line, g), centre(line, latin));
+                    assert!(g.y < -1.0, "a 6 pt run rises in a 10 pt line: {}", g.y);
+                }
+                _ => assert!(g.y.abs() < 1e-9, "Roman baseline keeps the run on the baseline: {}", g.y),
+            }
+        }
+    }
 }
 
 #[test]
diff --git a/crates/fonts/src/fontdb.rs b/crates/fonts/src/fontdb.rs
index 14441e144..0b87f23a1 100644
--- a/crates/fonts/src/fontdb.rs
+++ b/crates/fonts/src/fontdb.rs
@@ -117,8 +117,8 @@ pub struct FontFace {
     pub instance: Option<harfrust::ShaperInstance>,
     /// Basic Multilingual Plane coverage bitset, built on first use.
     bmp: std::sync::OnceLock<Box<[u64]>>,
-    /// The ideographic em box, read on first use.
-    em: std::sync::OnceLock<(f64, f64)>,
+    /// The ideographic em box and whether the `BASE` table gave it, read on first use.
+    em: std::sync::OnceLock<((f64, f64), bool)>,
     /// The font menu group and native family name, read on first use.
     group: std::sync::OnceLock<(FontGroup, Option<String>)>,
 }
@@ -263,7 +263,12 @@ impl FontFace {
     /// -120): `BASE` `idtp`/`ideo`, else the OS/2 typo ascender/descender, else the ascender and
     /// descender, the last two centred on one em.
     pub fn em_box(&self) -> (f64, f64) {
-        *self.em.get_or_init(|| crate::vertical::em_box(self))
+        self.em.get_or_init(|| crate::vertical::em_box(self)).0
+    }
+    /// The em box (top, bottom) the font's `BASE` table gives, in font units, y up; None without one.
+    pub fn base_em_box(&self) -> Option<(f64, f64)> {
+        let (em, from_base) = *self.em.get_or_init(|| crate::vertical::em_box(self));
+        from_base.then_some(em)
     }
     /// The font menu group the font is for and, for a CJK group, its family name in that language
     /// (see [`crate::FamilyInfo`]); read from the font once.
diff --git a/crates/fonts/src/vertical.rs b/crates/fonts/src/vertical.rs
index d360b6f2b..80f2e9833 100644
--- a/crates/fonts/src/vertical.rs
+++ b/crates/fonts/src/vertical.rs
@@ -55,11 +55,12 @@ impl<'a> VMetrics<'a> {
 
 /// The ideographic em box (top, bottom) in font units, y up: `BASE` `idtp`/`ideo`, else the OS/2
 /// typo ascender and descender, else the ascender and descender; the last two centred on one em.
-pub(crate) fn em_box(face: &FontFace) -> (f64, f64) {
+/// The flag says whether `BASE` gave it.
+pub(crate) fn em_box(face: &FontFace) -> ((f64, f64), bool) {
     let upem = face.upem;
     let font = face.skrifa();
     if let Some(b) = font.as_ref().and_then(|f| base_em_box(f, upem)) {
-        return b;
+        return (b, true);
     }
     let centred = |asc: f64, desc: f64| {
         let span = asc - desc;
@@ -68,10 +69,12 @@ pub(crate) fn em_box(face: &FontFace) -> (f64, f64) {
             (top, top - upem)
         })
     };
-    font.and_then(|f| f.os2().ok())
+    let em = font
+        .and_then(|f| f.os2().ok())
         .and_then(|t| centred(f64::from(t.s_typo_ascender()), f64::from(t.s_typo_descender())))
         .or_else(|| centred(face.ascent, -face.descent))
-        .unwrap_or((upem * 0.88, upem * -0.12))
+        .unwrap_or((upem * 0.88, upem * -0.12));
+    (em, false)
 }
 
 /// The em box from the `BASE` table's horizontal axis: the Han script's values, else the default