diff --git a/crates/tiff/src/reader.rs b/crates/tiff/src/reader.rs
index e1c6dd3a9..a644159b7 100644
--- a/crates/tiff/src/reader.rs
+++ b/crates/tiff/src/reader.rs
@@ -140,9 +140,10 @@ impl<'a> Ctx<'a> {
         }
         entries.sort_by_key(|e| e.tag);
         entries.dedup_by_key(|e| e.tag);
-        let next_pos = table + (n as usize).saturating_mul(entry_size);
-        let next = if n as usize == n_read {
-            match self.read_off(next_pos) {
+        // the next-IFD offset follows the whole table, so only a table read in full has one: a count far past the
+        // file (a BigTIFF's is 64-bit) must not reach the arithmetic (issue #1516)
+        let next = if n == n_read as u64 {
+            match n_read.checked_mul(entry_size).and_then(|len| table.checked_add(len)).and_then(|p| self.read_off(p)) {
                 Some(0) | None => 0,
                 Some(v) => base.checked_add(v).unwrap_or(0),
             }
diff --git a/crates/tiff/tests/roundtrip.rs b/crates/tiff/tests/roundtrip.rs
index 54fc82376..3b9a1bd1c 100644
--- a/crates/tiff/tests/roundtrip.rs
+++ b/crates/tiff/tests/roundtrip.rs
@@ -393,3 +393,37 @@ proptest! {
         prop_assert_eq!(t.ifds[0].f64s(501).unwrap().len(), v.len());
     }
 }
+
+/// A BigTIFF whose IFD says it has an enormous number of entries, with one readable, computed where the next-IFD
+/// offset would be from the advertised count: an add overflow, a panic in builds with overflow checks (issue
+/// #1516). The readable entry is kept and there is no next IFD; complete chains still link.
+#[test]
+fn bigtiff_with_an_enormous_entry_count_does_not_panic() {
+    for order in ORDERS {
+        for count in [u64::MAX, 1 << 62, 2] {
+            // little-endian bytes, reversed for big-endian files
+            let e = |le: &[u8]| -> Vec<u8> { if order == ByteOrder::Little { le.to_vec() } else { le.iter().rev().copied().collect() } };
+            let mut f = if order == ByteOrder::Little { b"II".to_vec() } else { b"MM".to_vec() };
+            for part in [e(&43u16.to_le_bytes()), e(&8u16.to_le_bytes()), e(&0u16.to_le_bytes()), e(&16u64.to_le_bytes()), e(&count.to_le_bytes())] {
+                f.extend(part);
+            }
+            // one entry: ImageWidth, LONG, 1 value (inline in the 8-byte field)
+            for part in [e(&tags::IMAGE_WIDTH.to_le_bytes()), e(&4u16.to_le_bytes()), e(&1u64.to_le_bytes()), e(&640u32.to_le_bytes())] {
+                f.extend(part);
+            }
+            f.extend([0; 4]);
+            let (ifd, next) = parse_ifd_at(&f, 16, order, 0, true, &ParseOptions::default()).unwrap();
+            assert_eq!(ifd.value(tags::IMAGE_WIDTH), Some(&Value::Long(vec![640])), "{order:?} {count}");
+            assert_eq!(next, 0, "{order:?} {count}");
+            let t = Tiff::parse(&f).unwrap();
+            assert_eq!(t.ifds.len(), 1);
+        }
+        // a complete chain of two IFDs still links
+        let mut a = IfdBuilder::new();
+        a.set(1000, Value::Short(vec![1]));
+        let mut b = IfdBuilder::new();
+        b.set(1000, Value::Short(vec![2]));
+        let t = Tiff::parse(&TiffWriter::new(order, true).write(&[a, b]).unwrap()).unwrap();
+        assert_eq!(t.ifds.len(), 2, "{order:?}");
+    }
+}