You can actually increase resolution and lower noise by oversampling and decimation.
2ˆ2n samples will give you n bits of extra resolution. So if you take 1024samples, you'd get 5 extra bits of resolution.
You do this by summing the ADC values (ints) in a long variable which you then bit-shift.
Here's a full explanation of the method: www.atmel.com/Images/doc8003.pdf
"It is important to remember that normal averaging does not increase the resolution of the conversion. Decimation, or Interpolation, is the averaging method, which combined with oversampling, which increases the resolution."