Data are presented characterizing the transverse mode behavior of AlAs/GaAs/InGaAs vertical-cavity surface-emitting lasers fabricated using a native-oxide process. The native-oxide process results in laser diodes with active regions defined to be 10, 8, and 4 mu m squares. We show that the transverse lasing mode is influenced by mirror reflectivity, with significant mode changes occurring with drive current for 8-10 mu m devices in the ranges of one to four times threshold. In smaller devices of 4 mu m square dimension, the transverse mode at threshold appears as a lowest order mode.