Theorems 3.1 and 3.2 as stated are incorrect. Corrected versions of these results are given below. Theorem 3.1 was concerned with an essentially complete class. Theorem 3.2 was concerned with a complete class. The correlations do affect a qualitative change in Theorem 3.2 in that now the result requires an assumption of a one dimensional exponential family and treats only a one-sided testing problem. There is essentially no qualitative change in Theorem 3.1, where the assumptions on distributions are minimal and there are no changes in the rest of the paper. The new version of Theorem 3.1 is also concerned with an essentially complete class. To describe this class let D* be the class of procedures characterized by (γ, ρ, π1*, T1*, T2*) where γ is the probability of stopping at time zero, ρ is the probability of rejection given that the procedure stopped at time zero and (π1*, T1*, T2*) are defined on pages 384 and 385, π1* ≥ c. A procedures δ corresponding to a (γ, ρ, π1*, T1*, T2*) lies in D* if whenever 0 ≤ < 1, δ is conditional Bayes with respect to (π1*, T1*, T2*) given that an observation had been taken.