This contribution investigates four members of the class of Detection, Identification, and Adaptation (DIA) estimators, which integrate parameter estimation with hypothesis testing. Using the framework of minimum mean penalty testing, we analyze and compare the misclosure-space partitionings of the traditional DIA procedure, which combines the overall model test with likelihood-ratio-based tests, and those maximizing the probabilities of correct hypothesis identification and parameter estimation. A constrained version of the latter, with the null hypothesis acceptance region fixed to the traditional procedure, is also examined. Our study focuses on cases where the biases under alternative hypotheses are fully known. Next to the conceptual comparison, we also assess, through a number of examples, misclosure-space partitionings and the probabilities of DIA estimators falling within a defined elliptical safety region. The results highlight the relationships and distinctions among the DIA estimators, revealing the influence of penalty functions, bias magnitude, safety region size, and false alarm probability.