A new graphical method for the fundamental design of pressure-swing distillation (PSD) and valid heat integration of the designed process is demonstrated based on a pinch analysis. As the minimum pressure constraint, the pinch pressure is determined by this graphical method to secure the necessary temperature driving force and circumvent the distillation boundaries. For a feasibility evaluation of heat-integrated PSD (HIPSD), the suggested approach requires visualization of the pinch temperature contours and the feasible composition region of an initial feed according to the pressure change and dynamic properties of ternary azeotropic systems. We thus carried out an in-depth examination by conducting case studies to show the feasible integration into HIPSD. The new insight is that the HIPSD system can have different pinch pressures depending on the column sequence or the separation order of pure components. In addition, the analysis verifies that energy-efficient HIPSD can be generated by considering pinch constraints.