Stirling-like thermoacoustic generators are external combustion engines that provide useful acoustic power in the absence of moving parts with high reliability and respect for the environment. The study of these systems involves a great complexity since the parameters that describe them, besides being numerous, present a high degree of coupling between them. This implies a great difficulty in characterizing the effects of any parametric variation on the performance of these devices. Due to the huge amount of data to analyze, the experiments and simulations required to address the problem involve high investments in time and resources, sometimes unaffordable. This article presents, how a sensitivity analysis applying the response surface methodology can be applied to optimize the feedback branch of a thermoacoustic Stirling-like engine. The proposed study is made by evaluating the comparative relevance of seven design variables. The dimensional reduction process identifies three significant factors: the frequency of operation, the internal diameter of compliance, and the inertance. Subsequently, the Response Surface Methodology is applied to assess the interaction effects of these three design parameters on the efficiency of the thermoacoustic engine, and an improvement of 6% has been achieved. The enhanced values given by the response surface methodology are validated using the DeltaEC software.