  We refine our earlier work on the existence and uniqueness of E-infinity
structures on K-theoretic spectra to show that at each prime p, the connective
Adams summand has an essentially unique structure as a commutative S-algebra.
For the p-completion we show that the McClure-Staffeldt model for it is
equivalent as an E-infinity ring spectrum to the connective cover of the
periodic Adams summand. We establish Bousfield equivalence between the
connective cover, c(E_n), of the Lubin-Tate spectrum E_n and BP<n> and propose
c(E_n) as an E-infinity approximation to the latter.
