diff --git a/crates/cos/src/document/reader.rs b/crates/cos/src/document/reader.rs
index 0bd4c980cd..8c52ea15de 100644
--- a/crates/cos/src/document/reader.rs
+++ b/crates/cos/src/document/reader.rs
@@ -417,10 +417,13 @@ impl Document {
             // Each section's rows are capped, so the chain is too: at most MAX_XREF_OBJECTS rows
             // merged in all, or the file is rebuilt from object headers, as when one section's
             // stream decodes past that. This counts rows merged, not the map's size, since a chain
-            // that relists the same objects costs as much to merge. A section's rows (its hybrid
-            // stream's included) never outnumber the rows the compact reader counts for it, and
-            // that reader stops at about a quarter of this cap: no chain within its limit is refused.
-            let Some(total) = merged_rows.checked_add(sect.len()).filter(|total| *total <= MAX_XREF_OBJECTS) else {
+            // that relists the same objects costs as much to merge. Rows set aside count too: they
+            // are kept for the whole chain, and a section can set aside nearly all it lists. A
+            // section's rows (its hybrid stream's included) never outnumber the rows the compact
+            // reader counts for it, and that reader stops at about a quarter of this cap: no chain
+            // within its limit is refused.
+            let rows = sect.len().saturating_add(odd.len());
+            let Some(total) = merged_rows.checked_add(rows).filter(|total| *total <= MAX_XREF_OBJECTS) else {
                 return Err(CosError::Syntax {
                     offset: usize::try_from(off).unwrap_or(usize::MAX),
                     detail: format!("cross-reference chain lists more than {MAX_XREF_OBJECTS} entries"),