Snapshots of the magnitude squared of the wavepackets taken after 10, 20 and 30 cycles of a laser pulse with turn-on times of 1, 4, 8 and 12 cycles. Authors investigate the structure of stabilized wavepackets for a two-dimensional model hydrogen atom interacting with an intense, high frequency laser pulse as a function of the laser pulse ellipticity and laser pulse rise- time. [See Patel et al. Fig. 4 for details].