It has been discovered that a dual bed process using two different catalysts for the selective hydrogenation of acetylene and/or methyl acetylene (MA) and/or propadiene (PD) in a light olefin-rich feedstream can be accomplished with less selectivity to making oligomers (green oil) as compared with existing commercial technologies, if a low oligomers selectivity catalyst is used first in the process. A palladium catalyst may be used as a second, sequential catalyst to further hydrogenate acetylene and/or MAPD while consuming at least a portion of the balance of the hydrogen present. The first catalyst should be different from the second catalyst.