Selick and Wu gave a functorial decomposition of $\Omega\Sigma X$ for path-connected, $p$-local \linebreak$\CW$\nbd-com\-plexes $X$ which obtained the smallest nontrivial functorial retract $A^{\min}(X)$ of $\Omega\Sigma X$. This paper uses methods developed by the second author in order to extend such functorial decompositions to the loops on coassociative co-$H$ spaces.