Polymeric foams with a gradient in density and morphology exhibit improved performances in terms of energy and sound absorption as compared to the uniformly foamed ones. In this work, we report an improvement of the gas-foaming method to obtain, for the first time, well-defined multi-graded foams. At variance with the conventional procedure which involve constant conditions, we impose a time varying partial pressure of the foaming agent. This allows to form a complex blowing agent concentration profile within the polymer, in turn giving a structured foam (tunable for specific applications) when supersaturation is attained by pressure drop. We use a unidimensional diffusion model to correlate the desired concentration profile to the pressure history imposed in the vessel. Following this new procedure, we used a periodic triangular pressure history of the blowing agent (CO2) to obtain a 3-layers and a 5-layers polystyrene foam. The produced foam layers were characterized by different void fractions, ranging between 0 and 90%, and pore sizes, from 50 to 500 microns.