Doubles methods are split into groups:
All the palindromic plain methods are here.
Note that I have only included symmetrical methods; there are more asymmetrical ones if you want them.
The definition of a method does not include its call, so on all numbers of bells except Doubles, you can use any call and still be ringing the same method. Doubles variations are an exception to this, which means that some ringers frown on them as not really being anything different from the parent method, but they are still great fun to ring. The other oddity about the variations is that, whereas in most methods the call only affects the change while the treble is leading, Doubles variations may change the whole of the work above the treble. This means that you have to be careful to call the calls in the right place - sometimes as early as when the treble is still in 4ths on the way in!
This information has been compiled from the Central Council "Collection of Doubles Methods" (part of which is on Tony Smith's website), Melvyn Hiller's "Collection of Doubles Methods and Variations" and an article by Tony Smith in the Ringing World of 1986 (page 896). I have also updated an electronic version (from 2000) of Melvyn Hiller's collection, with his kind permission; please credit him in any further dissemination.
I am always glad to hear of any corrections, amendments or additions to these records.