Many works infer finite-state models from execution logs. Large models are more accurate but also more difficult to present and understand. Small models are easier to present and understand but are less accurate. In this work we investigate the tradeoff between model size and accuracy in the context of the classic k-Tails model inference algorithm. First, we define mk-Tails, a generalization of k-Tails from one to many parameters, which enables fine-grained control over the tradeoff. Second, we extend mk-Tails with a reduction based on past-equivalence, which effectively reduces the size of the model without decreasing its accuracy. We implemented our work and evaluated its performance and effectiveness on models and generated logs from the literature.