diff --git a/lazy_dataset/core.py b/lazy_dataset/core.py
index ed8a59f..046e46b 100644
--- a/lazy_dataset/core.py
+++ b/lazy_dataset/core.py
@@ -3351,7 +3351,13 @@ def is_completed(self):
 
     def assess(self, example):
         seq_len = self.len_key(example)
-        return self.lower_bound <= seq_len <= self.upper_bound
+        return (
+            (self.lower_bound <= seq_len <= self.upper_bound)
+            and (
+                (self.max_total_size is None)
+                or ((len(self.data) + 1) * max(self.max_len, seq_len) <= self.max_total_size)
+            )
+        )
 
     def _append(self, example):
         super()._append(example)
diff --git a/tests/test_bucket.py b/tests/test_bucket.py
index b457f8f..c8d5764 100644
--- a/tests/test_bucket.py
+++ b/tests/test_bucket.py
@@ -19,3 +19,16 @@ def test_bucket():
     assert dynamic_batched_buckets == [
         [10, 5], [7, 8], [1, 2], [4, 3], [6, 9], [20], [1]
     ]
+
+
+def test_max_total_size():
+    examples = [6, 7, 9, 5, 6, 3, 7, 4]
+    examples = {str(j): i for j, i in enumerate(examples)}
+    ds = lazy_dataset.new(examples)
+
+    dynamic_batched_buckets = list(ds.batch_dynamic_time_series_bucket(
+        batch_size=3, len_key=lambda x: x, max_padding_rate=0.9, max_total_size=21,
+    ))
+    assert dynamic_batched_buckets == [
+        [6, 7, 5], [9, 6], [3, 7, 4]
+    ]