We investigate the effect of considering realistic propagation conditions different from classical Rice and Rayleigh fading on wireless physical layer security. Specifically, we study how the superposition of a number of dominant specular waves and diffusely propagating components impacts the achievable secrecy performance compared to conventional assumptions relying on the central limit theorem. We derive analytical expressions for the secrecy outage probability, which have similar complexity to other alternatives in the literature derived for simpler fading models. We provide very useful insights on the impact on physical layer security of (i) the number; (ii) the relative amplitudes and (iii) the overall power of the dominant specular components. We show that it is possible to obtain remarkable improvements on the system secrecy performance when: (a) the relative amplitudes of the dominant specular components for the eavesdropper channel are sufficiently large compared to those of the eavesdropper's channel eavesdropper, and (b) the power of Bob's dominant components is significantly larger than the power of the Eve's dominant components. Index Terms-generalized fading channels, mm-Wave, N-wave with diffuse power fading model, physical layer security.