The selectivity and activity of a silver-based olefin epoxidation catalyst is found to be a function of the pore size distribution in the alumina carrier on which it is deposited. Specifically it is found advantageous to provide a carrier which has a minimum of very large pores, (greater than 10 micrometers) and a water absorption of 35 to 55% and a surface area of at least 1.0 m2/g. A method of making such carriers is also described.