It is of prime importance to reveal the structure of wireless multi-access interference distributions to compute many performance bounds and metrics for wireless networks such as transmission capacity, outage probability and bit-errorrate. However, at the present, there are no closed form expressions for the multi-access interference distributions in wireless networks apart from a very special case. This paper presents a principled methodology towards the resolution of this bottleneck by establishing rates of convergence of the multi-access interference distribution to a Gaussian distribution for any given bounded power-law decaying path-loss function G.