Brewing one cup in a method usually used for larger batches

I have a brewer designed around larger batches, but most mornings I want a single mug. Using half the usual coffee and water changes the bed depth and pour behavior, and the cup comes out thin. I can make a full batch easily, but don't want the waste. Is there a sensible way to adapt a large pour-over cone for one cup, or is a smaller brewer one of those inexpensive tools that actually solves a real problem?