diff --git a/integration-tests/test_s3_buffering.py b/integration-tests/test_s3_buffering.py
new file mode 100644
index 00000000..6346c1ce
--- /dev/null
+++ b/integration-tests/test_s3_buffering.py
@@ -0,0 +1,23 @@
+from smart_open import open
+
+
+def read_bytes(url, limit):
+    bytes_ = []
+    with open(url, 'rb') as fin:
+        for i in range(limit):
+            bytes_.append(fin.read(1))
+
+    return bytes_
+
+
+def test(benchmark):
+    #
+    # This file is around 850MB.
+    #
+    url = (
+        's3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575541319511.97'
+        '/warc/CC-MAIN-20191216093448-20191216121448-00559.warc.gz'
+    )
+    limit = 1000000
+    bytes_ = benchmark(read_bytes, url, limit)
+    assert len(bytes_) == limit
diff --git a/smart_open/s3.py b/smart_open/s3.py
index 96bce460..93d61ffe 100644
--- a/smart_open/s3.py
+++ b/smart_open/s3.py
@@ -314,10 +314,6 @@ def read(self, size=-1):
         if self._eof:
             return self._read_from_buffer()
 
-        #
-        # Fill our buffer to the required size.
-        #
-        # logger.debug('filling %r byte-long buffer up to %r bytes', len(self._buffer), size)
         self._fill_buffer(size)
         return self._read_from_buffer(size)
 
@@ -430,7 +426,7 @@ def _read_from_buffer(self, size=-1):
         return part
 
     def _fill_buffer(self, size=-1):
-        size = size if size >= 0 else self._buffer._chunk_size
+        size = max(size, self._buffer._chunk_size)
         while len(self._buffer) < size and not self._eof:
             bytes_read = self._buffer.fill(self._raw_reader)
             if bytes_read == 0: