Recently, we have studied two important classes of algorithms requiring ±2b communications: ±2b-descend, and ±2b-ascend. Let N = 2n be the number of PEs in a SIMD hypercube which restricts all communications to a single fixed dimension at a time. In , we developed an efficient O(n) algorithm for the descend class. In , we obtained a simple O(n2/log n) algorithm for the ascend class, requiring O(log n) words of local memory per PE. In this paper, we present two new algorithms for the ascend class on a SIMD hypercube. The first algorithm runs in O(n1.5) time and requires O(1) space per PE. The second algorithm, which is discussed only briefly here, runs in O(n√n/log n) time and requires O(log n) space per PE.