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The support for Unicode strings in the email package
(notably MIMEText and Header class) is not uniform.
The behaviour with Unicode strings in Header is
documented but the interface is not good.
This code works, but it should not:
>>> h = Header.Header(u"àèìòù", charset="us-ascii")
>>> m = Message.Message()
>>> m["Subject"] = h
>>> print m.as_string()
Allowing this to work can cause confusion, I'm saying
that the charset is us-ascii, not utf-8.
With MIMEText I obtain:
m = MIMEText.MIMEText(u"àèìòù", _charset="us-ascii")
>>> print m.as_string()
[ exception ]
I think that the correct behaviour (for all functions
accepting strings) is:
- Do not accept plain str strings (8-bit).
 Accept only if they are plain ascii (7-bit).
- The charset specified should not be considered an 
 hint, but the charset I want to be used.
Regards Manlio Perillo

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The last example is not right.
Here is the correct one:
 >>> m = MIMEText.MIMEText(u"àèìòù", _charset="utf-8")
 
Traceback (most recent call last):
 File "<stdin>", line 1, in ?
 File "C:\Python2.4\lib\email\MIMEText.py", line 28, in
__init__
 self.set_payload(_text, _charset)
 File "C:\Python2.4\lib\email\Message.py", line 218, in
set_payload
 self.set_charset(charset)
 File "C:\Python2.4\lib\email\Message.py", line 260, in
set_charset
 self._payload = charset.body_encode(self._payload)
 File "C:\Python2.4\lib\email\Charset.py", line 366, in
body_encode
 return email.base64MIME.body_encode(s)
 File "C:\Python2.4\lib\email\base64MIME.py", line 136, in
encode
 enc = b2a_base64(s[i:i + max_unencoded])
UnicodeEncodeError: 'ascii' codec can't encode characters in
position 0-2: ordinal not in range(128)
So it seems that email.Message does not handle Unicode strings.
The code works if I set the charset to latin-1.

Confirmed on trunk.

It took me a while to figure out why latin-1 works. I turns out to be an accident: latin-1 uses quoted-printable encoding, and the email quoprimime module accidentally manages to quote unicode characters in the latin-1 range.
The Header example, as noted by the OP, is working as documented. This confusing interface isn't going to get fixed in the current email package. The equivalent email6 API will be cleaner.
The MIMEText portion is a duplicate of issue 1368247.