diff --git a/Lib/encodings/utf_16.py b/Lib/encodings/utf_16.py
index b145a5d..f3fadff 100644
--- a/Lib/encodings/utf_16.py
+++ b/Lib/encodings/utf_16.py
@@ -34,6 +34,22 @@
         codecs.IncrementalEncoder.reset(self)
         self.encoder = None
 
+    def getstate(self):
+        # state info we return to the caller:
+        # 0: stream is in natural order for this platform
+        # 2: endianness hasn't been determined yet
+        # (we're never writing in unnatural order)
+        return (2 if self.encoder is None else 0)
+
+    def setstate(self, state):
+        if state:
+            self.encoder = None
+        else:
+            if sys.byteorder == 'little':
+                self.encoder = codecs.utf_16_le_encode
+            else:
+                self.encoder = codecs.utf_16_be_encode
+
 class IncrementalDecoder(codecs.BufferedIncrementalDecoder):
     def __init__(self, errors='strict'):
         codecs.BufferedIncrementalDecoder.__init__(self, errors)
diff --git a/Lib/encodings/utf_8_sig.py b/Lib/encodings/utf_8_sig.py
index 697ba95..8784694 100644
--- a/Lib/encodings/utf_8_sig.py
+++ b/Lib/encodings/utf_8_sig.py
@@ -25,18 +25,24 @@
 class IncrementalEncoder(codecs.IncrementalEncoder):
     def __init__(self, errors='strict'):
         codecs.IncrementalEncoder.__init__(self, errors)
-        self.first = True
+        self.first = 1
 
     def encode(self, input, final=False):
         if self.first:
-            self.first = False
+            self.first = 0
             return codecs.BOM_UTF8 + codecs.utf_8_encode(input, self.errors)[0]
         else:
             return codecs.utf_8_encode(input, self.errors)[0]
 
     def reset(self):
         codecs.IncrementalEncoder.reset(self)
-        self.first = True
+        self.first = 1
+
+    def getstate(self):
+        return self.first
+
+    def setstate(self, state):
+        self.first = state
 
 class IncrementalDecoder(codecs.BufferedIncrementalDecoder):
     def __init__(self, errors='strict'):
diff --git a/Lib/test/test_io.py b/Lib/test/test_io.py
index 2874d79..b6bf686 100644
--- a/Lib/test/test_io.py
+++ b/Lib/test/test_io.py
@@ -2087,7 +2087,6 @@
 
         self.assertEqual(buffer.seekable(), txt.seekable())
 
-    @unittest.skip("Issue #6213 with incremental encoders")
     def test_append_bom(self):
         # The BOM is not written again when appending to a non-empty file
         filename = support.TESTFN
@@ -2103,7 +2102,6 @@
             with self.open(filename, 'rb') as f:
                 self.assertEquals(f.read(), 'aaaxxx'.encode(charset))
 
-    @unittest.skip("Issue #6213 with incremental encoders")
     def test_seek_bom(self):
         # Same test, but when seeking manually
         filename = support.TESTFN