If stars originate in transient bound clusters of moderate size, these clusters will decay due to dynamic interactions in which a hard binary forms and ejects most or all the other stars. When the cluster members are chosen at random from a reasonable initial mass function (IMF), the resulting binary characteristics do not match current observations. We find a significant improvement in the trends of binary properties from this scenario when an additional constraint is taken into account, namely that there is a distribution of total cluster masses set by the masses of the cloud cores from which the clusters form. Two distinct steps then determine final stellar masses - the choice of a cluster mass and the formation of the individual stars. We refer to this as a ``two-step'' IMF. Simple statistical arguments are used in this paper to show that a two-step IMF, combined with typical results from dynamic few-body system decay, tends to give better agreement between computed binary characteristics and observations than a one-step mass selection process.