def upload_new_files(staticdir, bucket):
    """
    Upload newer files recursively under `staticdir` to `bucket`.

    This assumes that the directory `staticdir` represents the root of
    the S3 bucket. `bucket` should be an instance of boto.s3.bucket.Bucket.

    Return a list of the files uploaded, with paths relative to `staticdir`.

    """
    allkeys = bucket.list()
    local_files_mtimes = get_keys_from_directory(staticdir)
    # `fmt` should be ISO 8601, but the time zone isn't parsed right when
    # given as %Z, so we hack it off below. Hopefully it's always Zulu time
    fmt = '%Y-%m-%dT%H:%M:%S.%f'
    # This is a dict of key_name -> [key_obj, key.last_modified]
    remote_files_mtimes_keys = dict(
        (
            k.name,
            [
                k,
                datetime.strptime(
                    k.last_modified[:-1],  # strip off Z at end
                    fmt)
            ]
        ) for k in allkeys)
    uploaded_files = []
    for filepath, local_mtime in local_files_mtimes.iteritems():
        if filepath in remote_files_mtimes_keys:
            the_key, remote_mtime = remote_files_mtimes_keys[filepath]
            # Skip file if local is older
            if remote_mtime > local_mtime:
                continue
        else:
            the_key = Key(bucket)
            the_key.key = filepath

        uploaded_files.append(filepath)
        the_key.set_contents_from_filename(os.path.join(staticdir, filepath))
        the_key.set_acl('public-read')
    return uploaded_files