You could translate each string to lowercase once --- lazily only when you need it, or as a prepass to the sort if you know you'll be sorting the entire collection of strings. There are several ways to attach this comparison key to the actual data being sorted, but these techniques should be addressed in a separate issue.
Note that this technique can be used not only to handle upper/lower case issues, but for other types of sorting such as locale specific sorting, or "Library-style" title sorting that ignores leading articles and otherwise normalizes the data before sorting it.
