We provide a lower bound for the coherence of the homotopy commutativity of the Brown-Peterson spectrum, BP, at a given prime p and prove that it is at least (2p(2) + 2p - 2) - homotopy commutative. We give a proof based on Dyer-Lashof operations that BP cannot be a Thom spectrum associated to n-fold loop maps to BSF for n = 4 at 2 and n = 2p + 4 at odd primes. Other examples where we obtain estimates for coherence are the Johnson - Wilson spectra, localized away from the maximal ideal and unlocalized. We close with a negative result on Morava-K-theory.