We continue our recent efforts to exploit the notion of a unitary isotope to study convex combinations of unitaries in an arbitrary JB*-algebra. Exact analogues of C*-algebraic results, due to R. V. Kadison, C. L. Olsen and G. K. Pedersen, are proved for general JB*-algebras. We show that if a contraction in a JB*-algebra is a convex combination of n unitaries, then it is also a mean of n unitaries. This generalizes a well known theorem of Kadison and Pedersen. Our methods also provide alternative proofs of other results for C*-algebras.