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Use of antiresonant structures is a proven, efficient method of improving lateral mode selectivity in VCSELs. In this paper, we analyze the impact of a low-refractive antiresonant oxide island buried in a top VCSEL mirror on the lasing conditions of lateral modes of different orders. By performing comprehensive thermal, electrical, and optical numerical analysis of the VCSEL device, we show the impact of the size and location of the oxide island on the current-crowding effect and compute threshold currents for various lateral modes. If the island is placed close to the cavity, the threshold shows strong oscillations, which for moderate island distances can be tuned to increase the side mode discrimination. We are therefore able to pinpoint the most important factors influencing mode discrimination and to identify oxide island parameters capable of providing single-lateral-mode emission.