Sometimes I want to enter a Unicode character I don't commonly use.  I can hunt the Web for its codepoint and use ctrl-shift-u in GTK, or I can hunt through a character map program and copy/paste.  If I use the character more than a couple times, perhaps I'll go to the effort of thinking up a shortcut for my .XCompose file.

It would be far more convenient if I could search the Unicode character list by name through UIM directly: press some shortcut, start typing a name, and get a candidate list of glyphs (even ordered MRU?).  This is the same basic idea as candidate lists in e.g. Anthy, so it seems appropriate to live in UIM.

I think ibus does something like this; there's little fanfare or documentation around it, but I found this screenshot: http://blog.du-a.org/wp-uploads/2011/06/ibus-gucharmap-search1.png
And a candidate window for an entire Unicode block: http://blog.du-a.org/wp-uploads/2011/06/ibus-gucharmap.png