diff --git a/awscli/customizations/s3/constants.py b/awscli/customizations/s3/constants.py
index d0877eed26b2..53bdc5cb4174 100644
--- a/awscli/customizations/s3/constants.py
+++ b/awscli/customizations/s3/constants.py
@@ -14,7 +14,4 @@
 CHUNKSIZE = 7 * (1024 ** 2)
 NUM_THREADS = 10
 QUEUE_TIMEOUT_WAIT = 0.2
-MAX_PARTS = 950
-MAX_SINGLE_UPLOAD_SIZE = 5 * (1024 ** 3)
-MAX_UPLOAD_SIZE = 5 * (1024 ** 4)
 MAX_QUEUE_SIZE = 1000
diff --git a/awscli/customizations/s3/s3handler.py b/awscli/customizations/s3/s3handler.py
index ec253aa4415c..5588faf1d673 100644
--- a/awscli/customizations/s3/s3handler.py
+++ b/awscli/customizations/s3/s3handler.py
@@ -17,7 +17,7 @@
 import sys
 
 from awscli.customizations.s3.constants import MULTI_THRESHOLD, CHUNKSIZE, \
-    NUM_THREADS, MAX_UPLOAD_SIZE, MAX_QUEUE_SIZE
+    NUM_THREADS, MAX_QUEUE_SIZE
 from awscli.customizations.s3.utils import find_chunksize, \
     operate, find_bucket_key, relative_path, PrintTask, create_warning
 from awscli.customizations.s3.executor import Executor
@@ -27,6 +27,9 @@
 
 
 LOGGER = logging.getLogger(__name__)
+# Maximum object size allowed in S3.
+# See: http://docs.aws.amazon.com/AmazonS3/latest/dev/qfacts.html
+MAX_UPLOAD_SIZE = 5 * (1024 ** 4)
 
 CommandResult = namedtuple('CommandResult',
                            ['num_tasks_failed', 'num_tasks_warned'])
diff --git a/awscli/customizations/s3/utils.py b/awscli/customizations/s3/utils.py
index a47dc2df2b1f..c9d929b2a4d1 100644
--- a/awscli/customizations/s3/utils.py
+++ b/awscli/customizations/s3/utils.py
@@ -24,14 +24,17 @@
 from dateutil.tz import tzlocal
 from botocore.compat import unquote_str
 
-from awscli.customizations.s3.constants import MAX_PARTS
-from awscli.customizations.s3.constants import MAX_SINGLE_UPLOAD_SIZE
 from awscli.compat import six
 from awscli.compat import PY3
 from awscli.compat import queue
 
 
-humanize_suffixes = ('KiB', 'MiB', 'GiB', 'TiB', 'PiB', 'EiB')
+HUMANIZE_SUFFIXES = ('KiB', 'MiB', 'GiB', 'TiB', 'PiB', 'EiB')
+MAX_PARTS = 10000
+# The maximum file size you can upload via S3 per request.
+# See: http://docs.aws.amazon.com/AmazonS3/latest/dev/UploadingObjects.html
+# and: http://docs.aws.amazon.com/AmazonS3/latest/dev/qfacts.html
+MAX_SINGLE_UPLOAD_SIZE = 5 * (1024 ** 3)
 
 
 def human_readable_size(value):
@@ -61,7 +64,7 @@ def human_readable_size(value):
     elif bytes_int < base:
         return '%d Bytes' % bytes_int
 
-    for i, suffix in enumerate(humanize_suffixes):
+    for i, suffix in enumerate(HUMANIZE_SUFFIXES):
         unit = base ** (i+2)
         if round((bytes_int / unit) * base) < base:
             return '%.1f %s' % ((base * bytes_int / unit), suffix)
diff --git a/tests/unit/customizations/s3/test_s3handler.py b/tests/unit/customizations/s3/test_s3handler.py
index 2105d3495770..d97a060306e8 100644
--- a/tests/unit/customizations/s3/test_s3handler.py
+++ b/tests/unit/customizations/s3/test_s3handler.py
@@ -23,6 +23,7 @@
 from awscli.customizations.s3.fileinfo import FileInfo
 from awscli.customizations.s3.tasks import CreateMultipartUploadTask, \
     UploadPartTask, CreateLocalFileTask
+from awscli.customizations.s3.utils import MAX_PARTS
 from tests.unit.customizations.s3.fake_session import FakeSession
 from tests.unit.customizations.s3 import make_loc_files, clean_loc_files, \
     make_s3_files, s3_cleanup, create_bucket, list_contents, list_buckets, \
@@ -697,7 +698,7 @@ def test_upload_stream_with_expected_size(self):
         # UploadPartTasks.
         changed_chunk_size = submitted_tasks[1][0][0]._chunk_size
         # New chunksize should have a total parts under 1000.
-        self.assertTrue(100000/changed_chunk_size < 1000)
+        self.assertTrue(100000 / float(changed_chunk_size) <= MAX_PARTS)
 
     def test_upload_stream_enqueue_upload_task(self):
         s3handler = S3StreamHandler(self.session, self.params)
diff --git a/tests/unit/customizations/s3/test_utils.py b/tests/unit/customizations/s3/test_utils.py
index 2a2355f252da..fde73e07a276 100644
--- a/tests/unit/customizations/s3/test_utils.py
+++ b/tests/unit/customizations/s3/test_utils.py
@@ -22,7 +22,7 @@
 from awscli.customizations.s3.utils import AppendFilter
 from awscli.customizations.s3.utils import create_warning
 from awscli.customizations.s3.utils import human_readable_size
-from awscli.customizations.s3.constants import MAX_SINGLE_UPLOAD_SIZE
+from awscli.customizations.s3.utils import MAX_SINGLE_UPLOAD_SIZE
 
 
 def test_human_readable_size():
@@ -102,8 +102,10 @@ def test_large_chunk(self):
         size because the original ``chunksize`` is too small.
         """
         chunksize = 7 * (1024 ** 2)
-        size = 8 * (1024 ** 3)
-        self.assertEqual(find_chunksize(size, chunksize), chunksize * 2)
+        size = 5 * (1024 ** 4)
+        # If we try to upload a 5TB file, we'll need to use 896MB part
+        # sizes.
+        self.assertEqual(find_chunksize(size, chunksize), 896 * (1024 ** 2))
 
     def test_super_chunk(self):
         """