A process of treating a catalyst composition containing palladium, an inorganic support, and a catalyst component, such as silver and/or a modifier such as alkali metal fluoride, is provided. The process involves contacting a catalyst composition with a first treating agent comprising carbon monoxide under a first treating condition to provide a treated catalyst composition. As an option, such treated catalyst composition can then be contacted with a second treating agent comprising a hydrogen-containing fluid under a second treating condition. The treated catalyst composition can be used in a selective hydrogenation process in which highly unsaturated hydrocarbons such as diolefins and/or alkynes are contacted with such treated catalyst composition in the presence of hydrogen to produce less unsaturated hydrocarbons such as monoolefins.