What are the voltages you are expecting to measure - in other words what is the relative error of the 15-20mV.
12-bit ADCs mean that the last bit is 1/4096 of the maximum range. If you are trying to measure (say) 0 to 5V then the bottom bit is +/- 1mV.
However, unless you are dealing with a *VERY* (electrical) noise-free environment, the best you can typically expect to measure with an ADC is something like 8 (+/-0.5%) or perhaps 10 bits (+/- 0.1%). That is just the nature of electrical signals .
Susan