Overregularization seen in child language learning, re verb tense constructs, involves abandoning correct behaviors for incorrect ones and later reverting to correct behaviors. Quite a number of other child development phenomena also follow this U-shaped form of learning, un- learning, and relearning. A decisive learner doesn’t do this and, in general, never abandons an hypothesis H for an inequivalent one where it later conjectures an hypothesis equivalent to H. The present paper shows that decisiveness is a real restriction on Gold’s model of iteratively (or in the limit) learning of grammars for languages from positive data. This suggests that natural U-shaped learning curves may not be a mere accident in the evolution of human learning, but may be necessary for learning. The result also solves an open problem. Second-time decisive learners conjecture each of their hypotheses for a language at most twice. By contrast, they are shown not to restrict Gold’s model of learning, and correspondingly, there is an apparent lack of re- ports in child development of the opposite, W-shaped learning curves.