We study a formation of patterns in Burgers-type equations endowed with a bounded but non-monotonic dissipative fluxes; $u_{t} + f(u)_{x} = \pm \nu Q(u_{x})_{x}, \, Q(s) = s/(1+s^{2})$. Issues of uniqueness, existence and smoothness of a solution are addressed. Asymptotic regions of solution are discussed and in particular, classical, and non-classical traveling waves with an embedded sub-shock are constructed.