In this paper the author studies the isoperimetric problem in R-n with perimeter density |x|(p) and volume density 1. We settle completely the case n = 2; completing a previous work by the author: we characterize the case of equality if 0 <= p <= 1 and deal with the case -infinity < p < -1 (with the additional assumption 0 is an element of Omega). In the case n >= 3 we deal mainly with the case -infinity < p < 0, showing among others that the results in 2 dimensions do not generalize for the range -n | 1 < p < 0.