We investigate the existence of MHD leaky waves in compressible and layered plasmas. We consider perturbations of complex frequency in a slab model with three layers. We develop a general method that includes the ‘cubic modes’ as well as other kinds of leaky waves, and allows us to derive many results in closed form. There are several physical mechanisms that can produce leakage. We give two numerical examples to exhibit the different behaviours that can arise. Finally we comment on the connection of the present results with those obtained by other authors, and correct some errors.