Starting with a p-local space X of l odd dimensional cells, l<p−1, Cooke, Harper, and Zabrodsky constructed an H-space Y with the property that H*(Y) is generated as an exterior Hopf algebra by H˜*(X). Cohen and Neisendorfer, and later Selick and Wu, reproduced this result with different constructions. We use the Selick and Wu approach to show that Y is homotopy associative and homotopy commutative if X is a suspension and l<p−2.