A porous inorganic composite oxide containing oxides of aluminum and of cerium and / or zirconium, and, optionally, oxides of one or more dopants selected from transition metals, rare earths, and mixtures thereof, and having a specific surface area, in m2 / g, after calcining at 1100° C. for 5 hours, of ≧0.8235[Al]+11.157 and a total pore volume, in cm3 / g, after calcining at 900° C. for 2 hours, of ≧0.0097[Al]+0.0647, wherein [Al] is the amount of oxides of aluminum, expressed as pbw Al2O3 per 100 pbw of the composite oxide; a catalyst containing one or more noble metals dispersed on the porous inorganic composite oxide; and a method for making the porous inorganic composite oxide.