The minimization of failure-inducing test cases is an important first step in the process of bug fixing. It helps focusing the expensive software engineering resources on the root of the problem by pruning down the excess from the input that is not contributing to the failure. Naturally, minimization is most helpful if it is automated. The original minimizing Delta Debugging algorithm and the follow-up Hierarchical Delta Debugging approach have been invented to give a solution to this challenge. Although automated, the minimization of inputs from real-life scenarios can take hours for both approaches. This paper builds on and improves the hierarchical minimization algorithm and experiments with a recursive variant called HDDr. After evaluating HDDr on various test cases, it turns out that it can give minimal results in 29–65% less time than the baseline hierarchical algorithm. On our largest test case, this means that the minimization process gets shorter by more than 4 hours.