We report on the analysis of high-precision space-based photometry of the roAp (rapidly oscillating Ap) stars HD 9289, HD 99563, and HD 134214. All three stars were observed by the MOST satellite for more than 25 days, allowing unprecedented views of their pulsation. We find previously unknown candidate frequencies in all three stars. We establish the rotation period of HD 9289 (8.5 d) for the first time and show that the star is pulsating in two modes that show different mode geometries. We present a detailed analysis of HD 99563's mode multiplet and find a new candidate frequency that appears to be independent of the previously known mode. Finally, we report on 11 detected pulsation frequencies in HD 134214, nine of which have never before been detected in photometry, and three of which are completely new detections. Thanks to the unprecedentedly small frequency uncertainties, the p-mode spectrum of HD 134214 can be seen to have a well-defined large frequency spacing similar to the well-studied roAp star HD 24712 (HR 1217).