Flat panel loudspeakers are a promising alternative to conventional loudspeakers. In particular, quasi-omnidirectional radiation at higher frequencies is stressed as an advantage of these systems compared to conventional speaker systems. However, this advantage can also be considered a disadvantage. Compared to that from conventional speakers with a flat and smooth on-axis and off-axis response, this wide radiation from flat panel loudspeakers occurs with an inconstant directivity factor, which can cause coloration and unusual spatial artifacts. This paper investigated the root causes of inhomogeneous directivity by using numerical methods. Based on these analyses, specific prototypes with various damping layups were built to overcome this problem. The additional damping layer reduces the off-axis radiation without significantly reducing the pressure level in the listening window. This approach is simple, robust, inexpensive and effective for improving the directivity of flat panel loudspeakers.