Boneh et al. showed at Crypto 99 that moduli of the form N = p^r q can be factored in polynomial time when r ≃ log(p). Their algorithm is based on Coppersmith’s technique for finding small roots of polynomial equations. In this paper we show that N = p^r q^s can also be factored in polynomial time when r or s is at least (log p)^3; therefore we identify a new class of integers that can be efficiently factored. We also generalize our algorithm to moduli with k prime factors N = \prod_{i=1}^k p_i^{r_i} ; we show that a non-trivial factor of N can be extracted in polynomial-time if one of the exponents r_i is large enough.