diff --git a/src/lib/solver.ts b/src/lib/solver.ts
index 2fa88bb..fe95ba0 100644
--- a/src/lib/solver.ts
+++ b/src/lib/solver.ts
@@ -265,23 +265,28 @@ type Primary =
     | { kind: "line"; datum: LineDatum }
     | { kind: "ellipse"; datum: EllipseDatum }
 
+function flaggedPrimary(d: Datum): Primary | null {
+    if (d.type === "rectangle" && d.isAxisReference) return { kind: "rect", datum: d }
+    if (d.type === "line" && d.axisRole) return { kind: "line", datum: d }
+    if (d.type === "ellipse" && d.isPrimary) return { kind: "ellipse", datum: d }
+    return null
+}
+
 function pickPrimary(datums: Datum[]): Primary {
     if (datums.length === 0) throw new Error("No datums provided.")
 
-    // User-flagged primary wins regardless of type priority. Rect's
-    // `isAxisReference` and line's `axisRole` carry axis semantics on top
-    // of "primary"; ellipse's `isPrimary` is a pure primary flag (ellipses
-    // don't define axis directions on their own).
+    // User-flagged primary wins regardless of type. The store
+    // (`setAxisRole`) enforces mutual exclusion across the three flag
+    // kinds — `RectDatum.isAxisReference`, `LineDatum.axisRole`, and
+    // `EllipseDatum.isPrimary` — so at most one datum is flagged at any
+    // time. Within a single datum only one of those fields can be set
+    // (discriminated union), so the check order inside `flaggedPrimary`
+    // is moot. If a future caller bypasses `setAxisRole` and creates
+    // multiple flagged datums, the first one in array order wins —
+    // deterministic but not semantic.
     for (const d of datums) {
-        if (d.type === "rectangle" && d.isAxisReference) {
-            return { kind: "rect", datum: d }
-        }
-        if (d.type === "line" && d.axisRole) {
-            return { kind: "line", datum: d }
-        }
-        if (d.type === "ellipse" && d.isPrimary) {
-            return { kind: "ellipse", datum: d }
-        }
+        const flagged = flaggedPrimary(d)
+        if (flagged) return flagged
     }
 
     const typeRank = (d: Datum): number =>
diff --git a/src/stores/app.ts b/src/stores/app.ts
index 9037130..9f7c4d8 100644
--- a/src/stores/app.ts
+++ b/src/stores/app.ts
@@ -113,16 +113,23 @@ export const useAppStore = defineStore("app", () => {
         id: string,
         role: "rect" | "x" | "y" | "ellipse" | null,
     ) {
-        // Clear any existing flag on other datums.
-        for (let i = 0; i < datums.value.length; i++) {
-            const d = datums.value[i]
-            if (!d || d.id === id) continue
-            if (d.type === "rectangle" && d.isAxisReference) {
-                datums.value[i] = { ...d, isAxisReference: false }
-            } else if (d.type === "line" && d.axisRole) {
-                datums.value[i] = { ...d, axisRole: null }
-            } else if (d.type === "ellipse" && d.isPrimary) {
-                datums.value[i] = { ...d, isPrimary: false }
+        // Only clear *other* datums' flags when actually assigning a new
+        // primary. A pure clear (`role === null`) must be a no-op against
+        // the rest of the set, otherwise clicking "None" on an unflagged
+        // line would silently strip the primary off whatever rect/ellipse
+        // legitimately holds it. The docstring guarantees "no-op if it
+        // wasn't set" for the target too — see the null branch below.
+        if (role !== null) {
+            for (let i = 0; i < datums.value.length; i++) {
+                const d = datums.value[i]
+                if (!d || d.id === id) continue
+                if (d.type === "rectangle" && d.isAxisReference) {
+                    datums.value[i] = { ...d, isAxisReference: false }
+                } else if (d.type === "line" && d.axisRole) {
+                    datums.value[i] = { ...d, axisRole: null }
+                } else if (d.type === "ellipse" && d.isPrimary) {
+                    datums.value[i] = { ...d, isPrimary: false }
+                }
             }
         }
         const idx = datums.value.findIndex((d) => d.id === id)
@@ -134,7 +141,7 @@ export const useAppStore = defineStore("app", () => {
                 datums.value[idx] = { ...target, isAxisReference: false }
             } else if (target.type === "line") {
                 datums.value[idx] = { ...target, axisRole: null }
-            } else {
+            } else if (target.type === "ellipse") {
                 datums.value[idx] = { ...target, isPrimary: false }
             }
             return