A novel method, binary countdown transformation, for generating integer compositions in parallel is proposed. Based on this method, an optimal and highly adaptive parallel algorithm for generating all compositions of integernis presented. The algorithm runs onpprocessors on a simple SIMD model requiring neither shared memory nor interconnection network and has a worst-case time complexity ofO(n2n−1/p), 1 ≤ p ≤ 2n−1. All the compositions generated are in lexicographic order. The proposed algorithm is superior to those built on generating combinations and set partitions.