diff --git a/lazip.py b/lazip.py
index 7cd1eda..e7940ec 100644
--- a/lazip.py
+++ b/lazip.py
@@ -229,6 +229,9 @@ class Filazy(ReadOnlyBinaryIOWrapper):
 
     def ensure(self, start: int, end: int) -> None:
         """Download bytes from start to end inclusively."""
+        offset = self.chunk_size - 1
+        start = max(0, min(start, end-offset))
+        end = min(self.length-1, max(end, start+offset))
         with self.stay():
             i, j = bisect_left(self.right, start), bisect_right(self.left, end)
             for start, end in self.merge(start, end, i, j):