diff --git a/moto/s3/models.py b/moto/s3/models.py
index a97e2862..9ab0a5b8 100644
--- a/moto/s3/models.py
+++ b/moto/s3/models.py
@@ -60,16 +60,15 @@ class FakeMultipart(object):
         self.parts = {}
         self.id = base64.b64encode(os.urandom(43)).replace('=', '').replace('+', '')
 
-
     def complete(self):
         total = bytearray()
+        last_part_name = len(self.list_parts())
 
         for part in self.list_parts():
+            if part.name != last_part_name and len(part.value) < 5242880:
+                return
             total.extend(part.value)
 
-        if len(total) < 5242880:
-            return
-
         return total
 
     def set_part(self, part_id, value):
diff --git a/tests/test_s3/test_s3.py b/tests/test_s3/test_s3.py
index f4a5ad18..8cbd489d 100644
--- a/tests/test_s3/test_s3.py
+++ b/tests/test_s3/test_s3.py
@@ -47,7 +47,7 @@ def test_multipart_upload():
     multipart.upload_part_from_file(BytesIO('hello'), 1)
     multipart.upload_part_from_file(BytesIO('world'), 2)
     # Multipart with total size under 5MB is refused
-    multipart.complete_upload().should.throw(S3ResponseError)
+    multipart.complete_upload.should.throw(S3ResponseError)
 
     multipart = bucket.initiate_multipart_upload("the-key")
     part1 = '0' * 5242880