We consider approximation algorithms for non-uniform buy-at-bulk network design problems. The first nontrivial approximation algorithm for this problem is due to Charikar and Karagiozova (STOC? 05); for an instance on h pairs their algorithm has an approximation guarantee of exp\left( {O\left( {\sqrt {\log h\log \log h} } \right)} \right) for the uniform-demand case, and logD ? exp\left( {O\left( {\sqrt {\log h\log \log h} } \right)} \right) for the general demand case, where D is the total demand. We improve upon this result, by presenting the first poly-logarithmic approximation for this problem. The ratio we obtain is O\left( {\log ^3 h \cdot \min \left\{ {\log D,\gamma \left( {h^2 } \right)} \right\}} \right) where h is the number of pairs and ?(n) is the worst case distortion in embedding the metric induced by a n vertex graph into a distribution over its spanning trees. Using the best known upper bound on \gamma(n) we obtain an O\left( {\min \left\{ {\log ^3 h \cdot \log D,\log ^5 h\log \log h} \right\}} \right) ratio approximation. We also give poly-logarithmic approximations for some variants of the singe-source problem that we need for the multicommodity problem.