diff --git a/crates/annot/src/draw.rs b/crates/annot/src/draw.rs
index 27f38f43f6..e36bf3a534 100644
--- a/crates/annot/src/draw.rs
+++ b/crates/annot/src/draw.rs
@@ -40,7 +40,15 @@ pub(crate) fn draw_appearance(doc: &mut Document, r: ObjRef) -> Result<(), Annot
 /// Draw the appearance for an annotation dictionary: the expensive half of [`set_appearance`].
 /// Pure from the dictionary and the objects it points at, so [`AppearanceCache`] can reuse it.
 fn build_appearance(doc: &Document, d: &Dict) -> Option<Stream> {
-    let mut stream = appearance::build(&with_direct_values(doc, d))?;
+    // References followed first. Where that turns up something the builder doesn't draw (a
+    // cloudy `/BE` on a square), the drawing made without them stays, rather than none.
+    let direct = with_direct_values(doc, d);
+    let built = appearance::build(&direct);
+    let mut stream = match (built, direct) {
+        (Some(stream), _) => stream,
+        (None, std::borrow::Cow::Owned(_)) => appearance::build(d)?,
+        (None, std::borrow::Cow::Borrowed(_)) => return None,
+    };
     // Picture-stamp restyling must retain the placement's page-axis correction.
     if d.get(b"PCPicture").is_some() {
         let matrix = d.get(b"AP").and_then(|ap| {
diff --git a/crates/annot/src/tests.rs b/crates/annot/src/tests.rs
index 6acb8ce742..28ab7e8fa7 100644
--- a/crates/annot/src/tests.rs
+++ b/crates/annot/src/tests.rs
@@ -1487,6 +1487,22 @@ fn indirect_border_style_and_colour_are_drawn() {
     assert_eq!(props.width, Some(6.0), "the properties show the width drawn");
 }
 
+/// A followed reference the builder can't draw (a cloudy border effect on a square, which it
+/// leaves alone) keeps the drawing made without it instead of none.
+#[test]
+fn an_undrawable_indirect_value_keeps_the_plain_drawing() {
+    let doc = document_of(&[
+        b"<< /Type /Catalog /Pages 2 0 R >>",
+        b"<< /Type /Pages /Kids [3 0 R] /Count 1 /MediaBox [0 0 200 200] >>",
+        b"<< /Type /Page /Parent 2 0 R /Annots [4 0 R] >>",
+        b"<< /Type /Annot /Subtype /Square /Rect [20 20 180 180] /BE 5 0 R /C [1 0 0] >>",
+        b"<< /S /C /I 1 >>",
+    ]);
+    let display = with_missing_appearances(&doc).expect("the square is still drawn");
+    let shown = list(&display, 0).remove(0);
+    assert!(ap_content(&display, &shown).contains("1 0 0 RG\n1 w\n"));
+}
+
 /// Following references copies a bounded number of values: an indirect array past the budget
 /// stays a reference (and the comment is not drawn from it), a chain that never ends is not
 /// followed, and links to other objects are never copied.