The invention is a process for epoxidizing an olefin with hydrogen and oxygen in the presence of a noble metal-containing titanium or vanadium zeolite and a modifier selected from the group consisting of carbon monoxide, methylacetylene, and propadiene. The process results in significantly reduced alkane by-product formed by the hydrogenation of olefin compared to processes that do not use the carbon monoxide, methylacetylene, and/or propadiene modifier.