There is described a process for producing ethylene/olefin interpolymers which, for a given melt index and density, have a reduced melting peak temperature (T.sub.m). The process involves contacting ethylene and at least one other olefin under polymerization conditions with an olefin polymerization catalyst and at least one modifier comprising at least one element from Group 15 and/or Group 16 in amounts sufficient to reduce the melting peak temperature of the ethylene/olefin interpolymer. Also described herein are novel ethylene/olefin interpolymers resulting from the process.