We provide new tradeoffs between approximation and running time for the decremental all-pairs shortest paths (APSP) problem. For undirected graphs with m edges and n nodes undergoing edge deletions, we provide two new approximate decremental APSP algorithms, one for weighted and one for unweighted graphs. Our first result is an algorithm that supports (2+ϵ)-approximate all-pairs constant-time distance queries with total update time ˜O(m1/2n3/2) when m=O(n5/3) (and m=n1+c for any constant c>0), or ˜O(mn2/3) when m=Ω(n5/3). Prior to our work the fastest algorithm for weighted graphs with approximation at most 3 had total ˜O(mn) update time providing a (1+ϵ)-approximation [Bernstein, SICOMP 2016]. Our technique also yields a decremental algorithm with total update time ˜O(nm3/4) supporting (2+ϵ,Wu,v)-approximate queries where the second term is an additional additive term and Wu,v is the maximum weight on the shortest path from u to v. Our second result is a decremental algorithm that given an unweighted graph and a constant integer k≥2, supports (1+ϵ,2(k−1))-approximate queries and has ˜O(n2−1/km1/k) total update time (when m=n1+c for any constant c>0). For comparison, in the special case of (1+ϵ,2)-approximation, this improves over the state-of-the-art algorithm by [Henzinger, Krinninger, Nanongkai, SICOMP 2016] with total update time of ˜O(n2.5). All of our results are randomized and work against an oblivious adversary.