With help from Martin v. Loewis, clarification is added for the
semantics of header chunks using byte and Unicode strings.
Specifically,

append(): When the given string is a byte string, charset (whether
specified explicitly in the argument list or implicitly via the
constructor default) is the encoding of the byte string, and a
UnicodeError will be raised if the string cannot be decoded with that
charset.  If s is a Unicode string, then charset is a hint specifying
the character set of the characters in the string.  In this case, when
producing an RFC 2822 compliant header using RFC 2047 rules, the
Unicode string will be encoded using the following charsets in order:
us-ascii, the charset hint, utf-8.

__init__(): Use the global USASCII Charset instance when the charset
argument is None.  Also, clarification in the docstring.

Also, use True/False where appropriate.
diff --git a/Lib/email/Header.py b/Lib/email/Header.py
index 70e0bac..0f2eb32 100644
--- a/Lib/email/Header.py
+++ b/Lib/email/Header.py
@@ -1,9 +1,11 @@
 # Copyright (C) 2002 Python Software Foundation
-# Author: che@debian.org (Ben Gertzfield)
+# Author: che@debian.org (Ben Gertzfield), barry@zope.com (Barry Warsaw)
 
 """Header encoding and decoding functionality."""
 
 import re
+from types import StringType, UnicodeType
+
 import email.quopriMIME
 import email.base64MIME
 from email.Charset import Charset
@@ -14,6 +16,12 @@
     # Python 2.1 spells integer division differently
     from email._compat21 import _floordiv
 
+try:
+    True, False
+except NameError:
+    True = 1
+    False = 0
+
 CRLFSPACE = '\r\n '
 CRLF = '\r\n'
 NL = '\n'
@@ -25,6 +33,9 @@
 ENCODE = 1
 DECODE = 2
 
+USASCII = Charset('us-ascii')
+UTF8 = Charset('utf-8')
+
 # Match encoded-word strings in the form =?charset?q?Hello_World?=
 ecre = re.compile(r'''
   =\?                   # literal =?
@@ -117,21 +128,19 @@
 class Header:
     def __init__(self, s=None, charset=None, maxlinelen=None, header_name=None,
                  continuation_ws=' '):
-        """Create a MIME-compliant header that can contain many languages.
+        """Create a MIME-compliant header that can contain many character sets.
 
-        Specify the initial header value in s.  If None, the initial header
-        value is not set.
+        Optional s is the initial header value.  If None, the initial header
+        value is not set.  You can later append to the header with .append()
+        method calls.  s may be a byte string or a Unicode string, but see the
+        .append() documentation for semantics.
 
-        Specify both s's character set, and the default character set by
-        setting the charset argument to a Charset object (not a character set
-        name string!).  If None, a us-ascii Charset is used as both s's
-        initial charset and as the default character set for subsequent
-        .append() calls.
-
-        You can later append to the header with append(s, charset) below;
-        charset does not have to be the same as the one initially specified
-        here.  In fact, it's optional, and if not given, defaults to the
-        charset specified in the constructor.
+        Optional charset serves two purposes: it has the same meaning as the
+        charset argument to the .append() method.  It also sets the default
+        character set for all subsequent .append() calls that omit the charset
+        argument.  If charset is not provided in the constructor, the us-ascii
+        charset is used both as s's initial charset and as the default for
+        subsequent .append() calls.
 
         The maximum line length can be specified explicit via maxlinelen.  For
         splitting the first line to a shorter value (to account for the field
@@ -143,7 +152,7 @@
         lines.
         """
         if charset is None:
-            charset = Charset()
+            charset = USASCII
         self._charset = charset
         self._continuation_ws = continuation_ws
         cws_expanded_len = len(continuation_ws.replace('\t', SPACE8))
@@ -186,20 +195,43 @@
         return not self == other
 
     def append(self, s, charset=None):
-        """Append string s with Charset charset to the MIME header.
+        """Append a string to the MIME header.
 
-        If charset is given, it should be a Charset instance, or the name of a
-        character set (which will be converted to a Charset instance).  A
-        value of None (the default) means charset is the one given in the
-        class constructor.
+        Optional charset, if given, should be a Charset instance or the name
+        of a character set (which will be converted to a Charset instance).  A
+        value of None (the default) means that the charset given in the
+        constructor is used.
+
+        s may be a byte string or a Unicode string.  If it is a byte string
+        (i.e. isinstance(s, StringType) is true), then charset is the encoding
+        of that byte string, and a UnicodeError will be raised if the string
+        cannot be decoded with that charset.  If `s' is a Unicode string, then
+        charset is a hint specifying the character set of the characters in
+        the string.  In this case, when producing an RFC 2822 compliant header
+        using RFC 2047 rules, the Unicode string will be encoded using the
+        following charsets in order: us-ascii, the charset hint, utf-8.
         """
         if charset is None:
             charset = self._charset
         elif not isinstance(charset, Charset):
             charset = Charset(charset)
+        # Normalize and check the string
+        if isinstance(s, StringType):
+            # Possibly raise UnicodeError if it can't e encoded
+            unicode(s, charset.get_output_charset())
+        elif isinstance(s, UnicodeType):
+            # Convert Unicode to byte string for later concatenation
+            for charset in USASCII, charset, UTF8:
+                try:
+                    s = s.encode(charset.get_output_charset())
+                    break
+                except UnicodeError:
+                    pass
+            else:
+                assert False, 'Could not encode to utf-8'
         self._chunks.append((s, charset))
 
-    def _split(self, s, charset, firstline=0):
+    def _split(self, s, charset, firstline=False):
         # Split up a header safely for use with encode_chunks.  BAW: this
         # appears to be a private convenience method.
         splittable = charset.to_splittable(s)
@@ -227,13 +259,13 @@
             # We can split on _maxlinelen boundaries because we know that the
             # encoding won't change the size of the string
             splitpnt = self._maxlinelen
-            first = charset.from_splittable(splittable[:splitpnt], 0)
-            last = charset.from_splittable(splittable[splitpnt:], 0)
+            first = charset.from_splittable(splittable[:splitpnt], False)
+            last = charset.from_splittable(splittable[splitpnt:], False)
         else:
             # Divide and conquer.
             halfway = _floordiv(len(splittable), 2)
-            first = charset.from_splittable(splittable[:halfway], 0)
-            last = charset.from_splittable(splittable[halfway:], 0)
+            first = charset.from_splittable(splittable[:halfway], False)
+            last = charset.from_splittable(splittable[halfway:], False)
         # Do the split
         return self._split(first, charset, firstline) + \
                self._split(last, charset)
@@ -248,7 +280,7 @@
             line = lines.pop(0)
             if firstline:
                 maxlinelen = self._firstlinelen
-                firstline = 0
+                firstline = False
             else:
                 #line = line.lstrip()
                 maxlinelen = self._maxlinelen
@@ -338,7 +370,7 @@
                 # There's no encoding for this chunk's charsets
                 _max_append(chunks, header, self._maxlinelen)
             else:
-                _max_append(chunks, charset.header_encode(header, 0),
+                _max_append(chunks, charset.header_encode(header),
                             self._maxlinelen, ' ')
         joiner = NL + self._continuation_ws
         return joiner.join(chunks)
@@ -363,6 +395,6 @@
         """
         newchunks = []
         for s, charset in self._chunks:
-            newchunks += self._split(s, charset, 1)
+            newchunks += self._split(s, charset, True)
         self._chunks = newchunks
         return self._encode_chunks()