We report new experimental evidence of the existence of double critical points in a binary system. Pressure-temperature data on the solubility of (polystyrene + acetaldehyde) were obtained using a low-angle light-scattering technique. Phase diagrams change from an UCST/LCST configuration showing a marked double maxima to an hour-glass shape with a "window of miscibility" as pressure decreases. Successful modeling of these unusual shapes was achieved by using a computation algorithm which incorporates a temperature- and concentration-dependent interaction parameter.