It is possible to enhance acoustic isolation of the device from the environment by appropriately controlling vibration of a device casing. Sound insulation efficiency of this technique for a rigid casing was confirmed by the authors in previous publications. In this paper, a light-weight casing is investigated, where vibrational couplings between walls are much greater due to lack of a rigid frame. A laboratory setup is described in details. The influence of the cross-paths on successful global noise reduction is considered. Multiple vibration actuators are installed on each of the casing walls. An adaptive control strategy based on the Least Mean Square (LMS) algorithm is used to update control filter parameters. Obtained results are reported, discussed, and conclusions for future research are drawn.