The addition of oxygen to methane/hydrogen/argon reactive ion etching (RIE) processes mitigate polymer deposition, and produce vertical etched sidewalls, This work contrasts the various ways in which the oxygen may be incorporated into methane/hydrogen/argon reactive ion etching of deep(>5 mu m) InGaAsP/InP multilayers. Three methods are investigated : a "continuous" process in which a fixed amount of oxygen is added to methane/hydrogen/argon for the duration of the etch, a "cyclical" process in which the methane/hydrogen/argon RIE processes alternates with oxygen RIE, and a hybrid process which incorporates the advantages of both former methods. These processes are applied to the fabrication of tall (>10 mu m) InGaAsP/InP quarter-wave mirrors for long-wavelength vertical-cavity lasers; the various benefits and limitations of the various approaches are discussed. It is found that the hybrid process allows formation of deeply etched structures (15 mu m) with vertical profiles.