diff --git a/tests/idempotence.rs b/tests/idempotence.rs
new file mode 100644
index 0000000..2f8423f
--- /dev/null
+++ b/tests/idempotence.rs
@@ -0,0 +1,29 @@
+//! Whether measuring a widget and then giving it the length it reported is a
+//! fixed point, which is what a span that sizes to its children needs.
+
+use iris::harness::Harness;
+use iris::prelude::*;
+
+#[test]
+fn a_wrapping_text_in_a_span_settles_on_one_width() {
+    let mut h = Harness::new((900, 600));
+    let words = "the quick brown fox jumps over the lazy dog and keeps on running \
+                 until it reaches the end of a rather long line of text";
+    let t = wtext(words).size(16).wrap(true).add(&mut h.rsc);
+    let filler = rect(Color::BLUE).add(&mut h.rsc);
+    h.set_root((t, filler).span(Dir::RIGHT));
+
+    let mut widths = Vec::new();
+    for _ in 0..6 {
+        let r = h.region(&t.id()).unwrap();
+        widths.push(r.bot_right.x - r.top_left.x);
+        // Redrawing it changes nothing about the state, so nothing may move.
+        h.rsc.widgets_mut().get_dyn_mut(t.id());
+        h.frame();
+    }
+    println!("widths over six frames: {widths:?}");
+    assert!(
+        widths.windows(2).all(|w| w[0] == w[1]),
+        "a repaint that changed nothing moved it: {widths:?}"
+    );
+}