In general, 15 buttons should be just fine. You have evidently figured out that you use a "comb" function whereby the transition points are calibrated to be halfway between the voltages corresponding to adjacent switches; you do not expect the voltages to match a certain specific value or narrow range.
I dislike the approach due to my experience of the unreliability of this system over time, as I have a number of failed appliances - computer monitors, MP3 players, microwave ovens and such - which use this method and fail over time as the contact resistance of the switches used fluctuates and as they develop leakage with moisture ingress (particularly bad for MP3 players which live in pockets!) leading to incorrect key detection and "ciphers" (where the OSD randomly starts up and drags one or more adjustments to the extreme).
On some occasions however, this appears to be not the fault of the keys, but of leakage in the ASIC (so it persists with the key assembly completely disconnected!) - you would presume the ATmega chips to be of better quality than to suffer that problem.