Meta-reasoning requires monitoring and controlling one's reasoning processes, and it often begins with an assessment of problem solvability. We explored whether "Judgments of Solvability (JOS)" for solvable and unsolvable anagrams discriminate and predict later problem-solving outcomes once anagrams solved during the JOS task are excluded. We also examined whether providing training via longer-duration anagrams improves JOS discrimination and predictiveness. In a two-phase paradigm, participants judged each anagram as "solvable," "not solvable," or "already solved" (S, NS, AS; JOS phase) then later attempted to solve the anagrams within 45 s (solving phase). Anagrams were presented in 4 blocks. In the "training groups," anagram duration started at 16 s and halved across blocks, whereas in the "no-training groups" anagram duration was always 2 s. Participants' S JOSs typically were discriminating after excluding anagrams that received AS JOSs, but training did not lead to better discrimination in the final block. Training improved AS JOS predictiveness, but not S JOS predictiveness. Thus, training increased solving during the JOS task rather than increasing JOS predictiveness. In Experiment 3 these findings replicated when both solvable and unsolvable anagrams were presented in the solving phase and no response deadline was set. Here, problem-solving outcomes and effort regulation (i.e., response times) were predicted by AS and NS JOSs, but not by S JOSs. Overall, although S JOSs were discriminating, they were not predictive of later problem solving or effort regulation--and this was true even after training with longer-duration anagrams.