I spent the morning up to my knees in php, because I had realised that the navigation inside this site was nowhere near flexible enough to demonstrate what I am talking about when I am discussing the way a mimi should work.
I had found the WordPress plug-in WPsnap, which allows you to display a category alphabetically (which I was already doing), but crucially spilts the entries up according to the first letter of their titles, and then presents you with a band of letters that you use to navigate the section.

This works brilliantly in theory, but not at all with the ways that I had altered my theme to accommodate what I had done so far. The only solution was to take what I had done apart and rebuild it.
I did this and duly got WPsnap working. Then I realised that ideally the user ought to be able to flip between a chronological view of the category and the alphabetical style. That was what took the time!
Finally I finished it and got it to work as I wanted. Just when I was about to turn my attention to something else I realised that there was still something missing. There should be an equivalent, date based, function available when you view the entries chronologically. This should probably be sorted by the year, except for this year and last year, which are sorted by the quarter.
I will add that later. When later is has yet to be decided…
Technical talk:
The theme I have made has an archive.php file which was where the previous customised loop lived. Because I was thinking originally that I may try to make WordPress choose between two files, according to whether or not the view should be alphabetical or chronological, I made a new category.php file. This is where the new loop was created.
In the event, I only needed one file, with a set of if…then…else statements, and some links that used Get to change a variable. The archive.php file is therefore surplus to requirements, but can stay where it is for the moment, as a piece of history in residence.
Johnny tells me that my quick and dirty method of grabbing the variable (which involves a line a little like: if ($_GET['saucy_devil']==666) is now officially bad practice, and something that I will have to rewrite when I upgrade to php5.
Ho hum, I say.
February 27, 2007:
I have decided that the default setting, the one that occurs whenever you open a new category page, should show the categories alphabetically. I therefore altered category.php slightly to flip values that control the default action. To make this clearer for the next time I have to look at it, I renamed the variable from show_snap to the currently more accurate hide_snap.