diff --git a/Lib/_pyio.py b/Lib/_pyio.py
index e3e7c3d..c9a7c5e 100644
--- a/Lib/_pyio.py
+++ b/Lib/_pyio.py
@@ -1436,6 +1436,15 @@
         self._snapshot = None  # info for reconstructing decoder state
         self._seekable = self._telling = self.buffer.seekable()
 
+        if self._seekable and self.writable():
+            position = self.buffer.tell()
+            if position != 0:
+                try:
+                    self._get_encoder().setstate(0)
+                except LookupError:
+                    # Sometimes the encoder doesn't exist
+                    pass
+
     # self._snapshot is either None, or a tuple (dec_flags, next_input)
     # where dec_flags is the second (integer) item of the decoder state
     # and next_input is the chunk of input bytes that comes next after the
@@ -1741,6 +1750,17 @@
                 raise IOError("can't restore logical file position")
             self._decoded_chars_used = chars_to_skip
 
+        # Finally, reset the encoder (merely useful for proper BOM handling)
+        try:
+            encoder = self._encoder or self._get_encoder()
+        except LookupError:
+            # Sometimes the encoder doesn't exist
+            pass
+        else:
+            if cookie != 0:
+                encoder.setstate(0)
+            else:
+                encoder.reset()
         return cookie
 
     def read(self, n=None):
diff --git a/Lib/test/test_io.py b/Lib/test/test_io.py
index 1a525dc..98dc711 100644
--- a/Lib/test/test_io.py
+++ b/Lib/test/test_io.py
@@ -1963,6 +1963,37 @@
 
         self.assertEqual(buffer.seekable(), txt.seekable())
 
+    def test_append_bom(self):
+        # The BOM is not written again when appending to a non-empty file
+        filename = support.TESTFN
+        for charset in ('utf-8-sig', 'utf-16', 'utf-32'):
+            with self.open(filename, 'w', encoding=charset) as f:
+                f.write('aaa')
+                pos = f.tell()
+            with self.open(filename, 'rb') as f:
+                self.assertEquals(f.read(), 'aaa'.encode(charset))
+
+            with self.open(filename, 'a', encoding=charset) as f:
+                f.write('xxx')
+            with self.open(filename, 'rb') as f:
+                self.assertEquals(f.read(), 'aaaxxx'.encode(charset))
+
+    def test_seek_bom(self):
+        # Same test, but when seeking manually
+        filename = support.TESTFN
+        for charset in ('utf-8-sig', 'utf-16', 'utf-32'):
+            with self.open(filename, 'w', encoding=charset) as f:
+                f.write('aaa')
+                pos = f.tell()
+            with self.open(filename, 'r+', encoding=charset) as f:
+                f.seek(pos)
+                f.write('zzz')
+                f.seek(0)
+                f.write('bbb')
+            with self.open(filename, 'rb') as f:
+                self.assertEquals(f.read(), 'bbbzzz'.encode(charset))
+
+
 class CTextIOWrapperTest(TextIOWrapperTest):
 
     def test_initialization(self):