Due to how the rewards are generated upon looting Beastmaster Durzag, it is possible to optimize Lil' Tuzzy's drop chance. Achto items and Mazcab ability codices are prioritized over the pet in the reward loot, and thus lowering the chance of those items contributes to increasing the chance of receiving Lil' Tuzzy. The gained boost to the drop rate is in the realm of only a couple of percent, but it is there if one is dedicated enough to take these steps to maximize their drop chance.