This paper examines two strategies that improve the beam pruning behavior of DNN acoustic models with only a negligible increase in model complexity. By augmenting the boosted MMI loss function used in sequence training with the weighted cross-entropy error, we achieve a real time factor (RTF) reduction of more than 13%. By directly incorporating a transition model into the DNN, which leads to a parameter size increase of less than 0.017%, we achieve a RTF reduction of 16%. Combining both techniques results in a RTF reduction of more than 23%. Both strategies, and their combination, also lead to small but statistically significant word error rate reductions.