diff --git a/crates/ui-egui/src/scenario.rs b/crates/ui-egui/src/scenario.rs
index 1f0d31b4..c035b58d 100644
--- a/crates/ui-egui/src/scenario.rs
+++ b/crates/ui-egui/src/scenario.rs
@@ -535,7 +535,7 @@ fn approx(got: f64, want: &Value, what: &str) -> Result<(), String> {
 /// Checks: `bodies` (count), `volume` / `area` (total, number or [value, rel tol]), `faces`,
 /// `features` (count), `errors` (timeline features in error, default 0), `dialog` (null: none
 /// open, or a word its kind must contain), `tool` (null or command id), `sketching` (bool),
-/// `selection` (count), `glyphs` ({constraint id: count}, none overlapping), `param` ({name: value}), `sketch_status` (solved|…), `dof`, `query`
+/// `selection` (count), `glyphs` ({constraint id: count}, none overlapping one another or a dimension value), `param` ({name: value}), `sketch_status` (solved|…), `dof`, `query`
 /// ({command, params?, path, value}: a command's result).
 pub fn check(h: &mut Harness, e: &Value) -> Result<(), String> {
     let doc = h.call("document.inspect", json!({"measure": true}))["result"].clone();
@@ -695,6 +695,10 @@ pub fn check(h: &mut Harness, e: &Value) -> Result<(), String> {
                     if let Some((b, _)) = g.iter().skip(i + 1).find(|(_, q)| q.distance(*p) < 14.0) {
                         return Err(format!("glyphs of {a} and {b} overlap at {p:?}"));
                     }
+                    let r = egui::Rect::from_center_size(*p, egui::vec2(14.0, 14.0));
+                    if let Some((d, _)) = crate::dim_view::text_rects().into_iter().find(|(_, t)| t.intersects(r)) {
+                        return Err(format!("glyph of {a} at {p:?} overlaps the value of dimension {d}"));
+                    }
                 }
             }
             "sketching" => {
diff --git a/crates/ui-egui/src/sketch_tools.rs b/crates/ui-egui/src/sketch_tools.rs
index 1c0eeaa9..61de6b4b 100644
--- a/crates/ui-egui/src/sketch_tools.rs
+++ b/crates/ui-egui/src/sketch_tools.rs
@@ -1000,7 +1000,13 @@ fn glyphs(app: &SolveApp, painter: &egui::Painter, proj: &Proj, hover: Option<Po
     let tk = crate::theme::Tokens::get();
     let picked = PICKED.with(|p| p.borrow().clone());
     // Where each glyph goes: beside its entity (to its left, away from the line), every entity
-    // of a two-entity constraint getting one; glyphs that would overlap step along.
+    // of a two-entity constraint getting one; glyphs that would overlap step along. A glyph
+    // that would sit on a dimension's value goes to the other side of its line.
+    let dim_texts: Vec<egui::Rect> = crate::dim_view::text_rects().into_iter().map(|(_, r)| r.expand(2.0)).collect();
+    let on_dim = |p: Pos2| {
+        let r = egui::Rect::from_center_size(p, egui::vec2(GLYPH, GLYPH));
+        dim_texts.iter().any(|d| d.intersects(r))
+    };
     let mut placed: Vec<(String, Pos2, Pos2)> = Vec::new();
     for c in &ss.sketch.constraints {
         if c.kind.is_dimension() {
@@ -1017,13 +1023,22 @@ fn glyphs(app: &SolveApp, painter: &egui::Painter, proj: &Proj, hover: Option<Po
                 None => egui::vec2(0.7, -0.7),
             };
             let step = if dir.is_some() { egui::vec2(side.y, -side.x) } else { egui::vec2(1.0, 0.0) };
-            let mut sp = base + side * (GLYPH * 0.9);
-            for _ in 0..12 {
-                if !placed.iter().any(|(_, q, _)| q.distance(sp) < GLYPH + 1.0) {
-                    break;
+            let free = |sp: Pos2| !placed.iter().any(|(_, q, _)| q.distance(sp) < GLYPH + 1.0);
+            let start = |s: egui::Vec2| base + s * (GLYPH * 0.9);
+            let side = if on_dim(start(side)) && !on_dim(start(-side)) { -side } else { side };
+            // Step along until clear of other glyphs, preferring a spot clear of dimension
+            // values too.
+            let settle = |avoid_dims: bool| {
+                let mut sp = start(side);
+                for _ in 0..12 {
+                    if free(sp) && !(avoid_dims && on_dim(sp)) {
+                        return Some(sp);
+                    }
+                    sp += step * (GLYPH + 2.0);
                 }
-                sp += step * (GLYPH + 2.0);
-            }
+                None
+            };
+            let sp = settle(true).or_else(|| settle(false)).unwrap_or_else(|| start(side) + step * (12.0 * (GLYPH + 2.0)));
             placed.push((c.id.clone(), sp, base));
         }
     }
diff --git a/crates/ui-egui/tests/scenarios/constraint_glyphs_clear_of_dimensions.json b/crates/ui-egui/tests/scenarios/constraint_glyphs_clear_of_dimensions.json
new file mode 100644
index 00000000..b879774a
--- /dev/null
+++ b/crates/ui-egui/tests/scenarios/constraint_glyphs_clear_of_dimensions.json
@@ -0,0 +1,9 @@
+[
+  {"call": "engine.execute", "params": {"command": "sketch.create", "params": {"plane": "XY"}}},
+  {"call": "engine.execute", "params": {"command": "sketch.rectangle.two_point", "params": {"p0": [0, 0], "p1": [10, 10]}}},
+  {"call": "engine.execute", "params": {"command": "sketch.dimension", "params": {"entities": ["l1"], "value": 10, "text_at": [5, -0.3]}}},
+  {"call": "engine.execute", "params": {"command": "sketch.dimension", "params": {"entities": ["l2"], "value": 10, "text_at": [10.3, 5]}}},
+  {"call": "ui.view", "params": {"view": "top"}},
+  {"call": "ui.view", "params": {"view": "fit"}},
+  {"expect": {"glyphs": {"k1": 1, "k2": 1, "k3": 1, "k4": 1}}}
+]