diff --git a/moto/s3/models.py b/moto/s3/models.py
index 5a665e27e..8c2a86f41 100644
--- a/moto/s3/models.py
+++ b/moto/s3/models.py
@@ -12,6 +12,7 @@ import codecs
 import random
 import string
 import tempfile
+import threading
 import sys
 import time
 import uuid
@@ -110,6 +111,7 @@ class FakeKey(BaseModel):
         self._value_buffer = tempfile.SpooledTemporaryFile(max_size=max_buffer_size)
         self._max_buffer_size = max_buffer_size
         self.value = value
+        self.lock = threading.Lock()
 
     @property
     def version_id(self):
@@ -117,8 +119,12 @@ class FakeKey(BaseModel):
 
     @property
     def value(self):
+        self.lock.acquire()
         self._value_buffer.seek(0)
-        return self._value_buffer.read()
+        r = self._value_buffer.read()
+        r = copy.copy(r)
+        self.lock.release()
+        return r
 
     @value.setter
     def value(self, new_value):
@@ -130,6 +136,7 @@ class FakeKey(BaseModel):
         if isinstance(new_value, six.text_type):
             new_value = new_value.encode(DEFAULT_TEXT_ENCODING)
         self._value_buffer.write(new_value)
+        self.contentsize = len(new_value)
 
     def copy(self, new_name=None, new_is_versioned=None):
         r = copy.deepcopy(self)
@@ -157,6 +164,7 @@ class FakeKey(BaseModel):
         self.acl = acl
 
     def append_to_value(self, value):
+        self.contentsize += len(value)
         self._value_buffer.seek(0, os.SEEK_END)
         self._value_buffer.write(value)
 
@@ -229,8 +237,7 @@ class FakeKey(BaseModel):
 
     @property
     def size(self):
-        self._value_buffer.seek(0, os.SEEK_END)
-        return self._value_buffer.tell()
+        return self.contentsize
 
     @property
     def storage_class(self):
@@ -249,6 +256,7 @@ class FakeKey(BaseModel):
         state = self.__dict__.copy()
         state["value"] = self.value
         del state["_value_buffer"]
+        del state["lock"]
         return state
 
     def __setstate__(self, state):
@@ -258,6 +266,7 @@ class FakeKey(BaseModel):
             max_size=self._max_buffer_size
         )
         self.value = state["value"]
+        self.lock = threading.Lock()
 
 
 class FakeMultipart(BaseModel):
@@ -284,7 +293,7 @@ class FakeMultipart(BaseModel):
                 etag = etag.replace('"', "")
             if part is None or part_etag != etag:
                 raise InvalidPart()
-            if last is not None and len(last.value) < UPLOAD_PART_MIN_SIZE:
+            if last is not None and last.contentsize < UPLOAD_PART_MIN_SIZE:
                 raise EntityTooSmall()
             md5s.extend(decode_hex(part_etag)[0])
             total.extend(part.value)