Ptychography has been shown to be an efficient phase contrast imaging technique for scanning transmission electron microscopes (STEM). STEM-ptychography uses a fast pixelated detector to collect a “4-dimensional” dataset consisting of a 2D electron diffraction pattern at every probe position of a 2D raster-scan. This 4D dataset can be used to recover the phase-image. Current camera technology, unfortunately, can only achieve a frame rate of a few thousand detector frames-per-second (fps), which means that the acquisition time of the 4D dataset is up to 1000× slower than the scanning speed in a conventional STEM, thereby limiting the potential applications of this method for dose-fragile and dynamic specimens. In this letter, we demonstrate that subsampling provides an effective method for optimizing ptychographic acquisition by reducing both the number of detector-pixels and the number of probe positions. Subsampling and recovery of the 4D dataset are shown using an experimental 4D dataset with randomly removed detector-pixels and probe positions. After compressive sensing recovery, Wigner distribution deconvolution is applied to obtain phase-images. Randomly sampling both the probe positions and the detector at 10% gives sufficient information for phase-retrieval and reduces acquisition time by 100×, thereby making STEM-ptychography competitive with conventional STEM.