Abstract In this paper we present a novel alternate model for distillation cascades without integer variables. This allows for optimization of highly nonlinear process flowsheets with embedded distillation columns, modeled with rigorous mass, equilibrium, summation and heat (MESH) equations. Instead of reformulating the famous MINLP distillation column model as an MPCC (mathematical program with complementarity constraints), bypass streams are added to the distillation cascade superstructure. If a tray is fully active the bypass streams are inactive (zero flow) and the standard MESH results are obtained. If a tray is completely inactive all of the flow bypasses the tray, resulting in no separation. As a result the interior of the bypass fraction (analogous to integer variables in the MINLP model) is well defined. In fact a partially bypassed stream is physically realizable (although inefficient). For this reason we postulate that this alternate model with bypass leads to well-behaved solution strategies.