We consider the problem of compact routing with slack in networks of low doubling dimension. Namely, we seek name-independent routing schemes with (1+) stretch and polylogarithmic storage at each node: since existing lower bound precludes such a scheme, we relax our guarantees to allow for (i) a small fraction of nodes to have large storage, say size of O(n log n) bits, or (ii) a small fraction of source-destination pairs to have larger, but still constant, stretch. In this paper, given any constant (0,1), any (1/ polylog n) and any connected edge-weighted undirected graph G with doubling dimension α O(log log n) and arbitrary node names, we present 1. a (1+)-stretch name-independent routing scheme for G with polylogarithmic packet header size, and with (1-)n nodes storing polylogarithmic size routing tables each and the remaining n nodes storing O(nlog n)-bit routing tables each. 2. a name-independent routing scheme for G with polylogarithmic storage and packet header size, and with stretch (1+) for (1-α n source nodes and (9+) for the remaining α n source nodes.. These results are to be contrasted with our lower bound from PODC 2006, where we showed that stretch 9 is asymptotically optimal for name-independent compact routing schemes in networks of constant doubling dimension.