Managed to get WordPress installed on a 1&1 account. Not actually too difficult, but the catch is that 1&1 offers frame and HTTP redirects from purchased domain names to separate areas. After a lot of failed attempts (which typically required using phpmysql admin to directly change the values in the database), I discovered the correct sequence to get good URLs:
Choose frame redirection under the 1&1 hostname to the correct webspace name
Edit the wordpress fields so that the Blog address (URL) points to the ‘other’ name.
Not a lot of detail here, but this is what worked for me.