The reduction of the emitted noise from vehicles is a primary issue for automotive OEM’s due to the constant evolution of the noise regulations. As the noise generated by the powertrain remains one of the major noise sources at low/mid vehicle velocities, focus is set on efficient methods to control this source. Acoustic treatments and covers, made of multi-layered trimmed panels, are frequently selected to control the radiated sound and its directivity. In this context, numerical acoustic simulation is an attractive approach as efficient methodologies are available to study the acoustic radiation of powertrain units in working conditions (up to 6500 RPM nd frequencies up to 4 kHz). Moreover, handling acoustically-treated covers in such simulations has a low impact on the computational cost. Nevertheless, the robust design of treatments (optimization and variability analysis) is more challenging as it implies multiple acoustic radiation analyses, leading to impracticable computational times in industrial conditions. This paper presents a framework for the efficient solution of acoustic radiation models where only a localized part of the model is subjected to design changes. Based on the static condensation of the exterior acoustic problem onto the surface of the acoustic treatments, a model reduction is achieved that allows for a substantial speed up of the optimization loop and/or the variability analysis (especially at high frequencies), as the residual model involving the design changes is much smaller than the global model. The numerical performance of the proposed methodology is demonstrated on an industrial engine radiation application, using the Actran acoustic simulation environment.