We study the optimal Stein error exponent for one-way distributed hypothesis testing under a communication rate constraint. We establish exact rate-exponent tradeoffs for new classes of finite-alphabet sources, including a complete single-letter characterization for every pair of strictly positive binary joint distributions as well as testing-against-dependence. Our converse analysis refines the auxiliary-receiver method through three complementary steps. First, we establish an information-projection identity that identifies the posterior-divergence optimization in an existing converse with Han's exponent functional. Second, we obtain an additional excess-rate branch by retaining a mutual-information term discarded in the usual rate relaxation. Third, we develop a two-telescope upper bound whose auxiliary variables are coupled through a joint rate constraint. Combining these bounds with information-geometric matching conditions yields exact exponents for three classes of sources by matching the achievable bounds of Han and Shimokawa-Han-Amari.

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