This paper investigates strategies to limit the cost of switching the cache in the context of an optimistic discrete caching problem. We have chosen as a starting point the current state-of-the-art in optimistic discrete caching, the Optimistic Follow-The-Perturbed-Leader (OFTPL) algorithm. We propose two strategies that attempt to limit this cost. The first approach sets a lower bound for the perturbation factor, thus including a mandatory amount of noise in the optimization of the cache state. The second approach investigates dynamically updating the perturbation factor to increase the switching cost, hence allowing the algorithm to adapt to the scenario at hand. Therefore, to the best of our knowledge, we design the first optimistic discrete caching algorithm that attempts to optimize the switching cost. Finally, we experiment and evaluate our solutions while highlighting their strengths and limitations.