diff --git a/crates/doc/src/table.rs b/crates/doc/src/table.rs
index d3c028067..76911dd4f 100644
--- a/crates/doc/src/table.rs
+++ b/crates/doc/src/table.rs
@@ -48,6 +48,12 @@ impl Row {
     pub fn first_grid(&self) -> usize {
         (self.props.grid_before as usize).min(MAX_COLS)
     }
+
+    /// Grid columns `w:gridAfter` leaves empty after the row's last cell, bounded as the DOCX
+    /// reader bounds them (a native document can say anything).
+    pub fn grid_after(&self) -> usize {
+        (self.props.grid_after as usize).min(MAX_COLS)
+    }
 }
 
 #[derive(Clone, Debug, PartialEq, Serialize, Deserialize, Default)]
@@ -97,7 +103,8 @@ impl Table {
     }
 
     pub fn cols(&self) -> usize {
-        let row_cols = |r: &Row| r.first_grid() + r.cells.iter().map(Cell::span).sum::<usize>() + r.props.grid_after as usize;
+        let row_cols =
+            |r: &Row| r.first_grid().saturating_add(r.cells.iter().map(Cell::span).fold(0, usize::saturating_add)).saturating_add(r.grid_after());
         self.grid.len().max(self.rows.iter().map(row_cols).max().unwrap_or(0))
     }
 
diff --git a/crates/layout/src/lib.rs b/crates/layout/src/lib.rs
index f639078ec..448182990 100644
--- a/crates/layout/src/lib.rs
+++ b/crates/layout/src/lib.rs
@@ -4967,6 +4967,8 @@ mod tests_autospace;
 #[cfg(test)]
 mod tests_bidi;
 #[cfg(test)]
+mod tests_budget;
+#[cfg(test)]
 mod tests_complex;
 #[cfg(test)]
 mod tests_grid;
diff --git a/crates/layout/src/table.rs b/crates/layout/src/table.rs
index d2e24e891..169eda6b9 100644
--- a/crates/layout/src/table.rs
+++ b/crates/layout/src/table.rs
@@ -537,7 +537,7 @@ pub fn layout_table(ctx: &mut Ctx, story: StoryRef, t: &Table, path: &[u32], ava
             let row_borders = row.props.exceptions.as_ref().and_then(|e| e.borders).unwrap_or_default();
             // A row that skips grid columns (`w:gridBefore`/`w:gridAfter`) has its edge at its own
             // first and last cell.
-            let (first_g, last_g) = (g == row.first_grid(), g + span >= ncols.saturating_sub(row.props.grid_after as usize));
+            let (first_g, last_g) = (g == row.first_grid(), g + span >= ncols.saturating_sub(row.grid_after()));
             let rb = look.map(|l| region_borders(&l.borders, (ri, nrows), (first_g, last_g))).unwrap_or_default();
             let mut borders = Borders {
                 top: edge(cb.top.or(if ri == 0 { row_borders.top } else { row_borders.between }).or(rb.top), ri == 0, tb.top, tb.between),
@@ -1170,7 +1170,7 @@ fn column_content(ctx: &mut Ctx, t: &Table, style: Option<&TableStyleProps>, dep
 /// columns, width in points). Column widths make room for them like for an empty cell.
 fn row_gaps(row: &Row, end: usize) -> impl Iterator<Item = (usize, usize, f32)> {
     let p = &row.props;
-    [(0, row.first_grid(), p.w_before), (end, p.grid_after as usize, p.w_after)]
+    [(0, row.first_grid(), p.w_before), (end, row.grid_after(), p.w_after)]
         .into_iter()
         .filter(|&(_, n, _)| n > 0)
         .filter_map(|(g, n, w)| w.filter(|w| w.is_finite() && *w > 0.0).map(|w| (g, n, w.min(1584.0))))
diff --git a/crates/layout/src/tests_budget.rs b/crates/layout/src/tests_budget.rs
new file mode 100644
index 000000000..c98efc3d6
--- /dev/null
+++ b/crates/layout/src/tests_budget.rs
@@ -0,0 +1,24 @@
+//! Hostile documents whose layout work or memory would otherwise grow far past their size: each
+//! is bounded by a cap, and real documents stay well under it.
+
+use super::*;
+use wordcraft_doc::Block;
+use wordcraft_doc::table::{MAX_COLS, Table};
+
+fn lay(doc: &Document) -> DocLayout {
+    let mut c = LayoutCache::new();
+    layout(doc, &mut c, &LayoutOptions::default())
+}
+
+#[test]
+fn a_huge_grid_after_is_bounded_like_the_docx_readers() {
+    // A native document can say a row leaves four billion columns empty after its cells.
+    let mut t = Table::new(1, 2, 468.0);
+    t.rows[0].props.grid_after = u32::MAX;
+    t.grid.clear();
+    assert!(t.cols() <= 2 + MAX_COLS, "{} columns", t.cols());
+    let mut d = Document::from_text("");
+    d.insert_block(StoryRef::Body, &Path::top(1), Block::Table(t)).unwrap();
+    let l = lay(&d);
+    assert!(l.pages[0].items.iter().any(|i| matches!(i, Placed::Cell { row: 0, cell: 1, .. })));
+}