  In this short note we consider mixed short-long range independent bond
percolation models on $\Z^{k+d}$. Let $p_{uv}$ be the probability that the edge
$(u,v)$ will be open. Allowing a $x,y$-dependent length scale and using a
multi-scale analysis due to Aizenman and Newman, we show that the long distance
behavior of the connectivity $\tau_{xy}$ is governed by the probability
$p_{xy}$. The result holds up to the critical point.
