We report finite difference time domain simulations of GaAs-Al0.95Ga0.05As micropillars containing single quantum dots capped with SiO2 microlenses of differing shapes and heights, finding oscillations of relevant properties as functions of lens thickness, with the Q factor and Purcell factor varying by a factor of ~2, while the mode field diameter and numerical aperture change over a 10% range. Such structures could be realised by modifying our previously reported direct-write lithography process to retain some of the hard mask on top of the pillar, shaping the emission of these single photon sources to be more efficiently collected into a single mode fibre.