diff --git a/Lib/tarfile.py b/Lib/tarfile.py
--- a/Lib/tarfile.py
+++ b/Lib/tarfile.py
@@ -228,17 +228,17 @@
     signed_chksum = 256 + sum(struct.unpack_from("148b8x356b", buf))
     return unsigned_chksum, signed_chksum
 
-def copyfileobj(src, dst, length=None, exception=OSError):
+def copyfileobj(src, dst, length=None, exception=OSError, bufsize=None):
     """Copy length bytes from fileobj src to fileobj dst.
        If length is None, copy the entire content.
     """
+    BUFSIZE = bufsize or 16 * 1024
     if length == 0:
         return
     if length is None:
-        shutil.copyfileobj(src, dst)
+        shutil.copyfileobj(src, dst, BUFSIZE)
         return
 
-    BUFSIZE = 16 * 1024
     blocks, remainder = divmod(length, BUFSIZE)
     for b in range(blocks):
         buf = src.read(BUFSIZE)
@@ -1403,7 +1403,8 @@
 
     def __init__(self, name=None, mode="r", fileobj=None, format=None,
             tarinfo=None, dereference=None, ignore_zeros=None, encoding=None,
-            errors="surrogateescape", pax_headers=None, debug=None, errorlevel=None):
+            errors="surrogateescape", pax_headers=None, debug=None,
+            errorlevel=None, copybufsize=None):
         """Open an (uncompressed) tar archive `name'. `mode' is either 'r' to
            read from an existing archive, 'a' to append data to an existing
            file or 'w' to create a new file overwriting an existing one. `mode'
@@ -1459,6 +1460,7 @@
             self.errorlevel = errorlevel
 
         # Init datastructures.
+        self.copybufsize = copybufsize
         self.closed = False
         self.members = []       # list of members as TarInfo objects
         self._loaded = False    # flag if all members have been read
@@ -1963,10 +1965,10 @@
         buf = tarinfo.tobuf(self.format, self.encoding, self.errors)
         self.fileobj.write(buf)
         self.offset += len(buf)
-
+        bufsize=self.copybufsize
         # If there's data to follow, append it.
         if fileobj is not None:
-            copyfileobj(fileobj, self.fileobj, tarinfo.size)
+            copyfileobj(fileobj, self.fileobj, tarinfo.size, bufsize=bufsize)
             blocks, remainder = divmod(tarinfo.size, BLOCKSIZE)
             if remainder > 0:
                 self.fileobj.write(NUL * (BLOCKSIZE - remainder))
@@ -2148,13 +2150,14 @@
         """
         source = self.fileobj
         source.seek(tarinfo.offset_data)
+        bufsize = self.copybufsize
         with bltn_open(targetpath, "wb") as target:
             if tarinfo.sparse is not None:
                 for offset, size in tarinfo.sparse:
                     target.seek(offset)
-                    copyfileobj(source, target, size, ReadError)
+                    copyfileobj(source, target, size, ReadError, bufsize)
             else:
-                copyfileobj(source, target, tarinfo.size, ReadError)
+                copyfileobj(source, target, tarinfo.size, ReadError, bufsize)
             target.seek(tarinfo.size)
             target.truncate()