Phase-Diverse Speckle (PDS) is a short-exposure data- collection and processing technique that blends phase- diversity and speckle- imaging concepts. PDS has been successfully used for solar astronomy to achieve near diffraction-limited resolution in ground-based imaging of solar granulation. Variants of PDS that involve narrow-band, spectroscopic, and polarimetric data provide more information observations. We present results from processing data collected with the 76-cm Richard B. Dunn Solar Telescope (DST) on Sacramento Peak, NM. Three-channel data sets consisting of a pair of phase-diverse images of the solar continuum and a narrow-band image were collected over spans of 15 - 20 minutes. Point-spread functions that are estimated from the PDS data are used in a multi-frame deconvolution algorithm to correct the narrow-band imagery. The data were processed into a number of time series. A rare, short-lived continuum bright point with a peak intensity at a factor of 2.1 above the mean intensity in the continuum was observed in one such sequence. The field of view spans multiple isoplanatic patches, and strategies for processing these large fields were developed. We will discuss these methods along with other techniques that were explored for accelerating the processing. Finally, we show the first PDS reconstruction of adaptive-optics (AO) compensated solar granulation taken at the DST. As expected, we find that these data are less aberrated and, thus, the use of AO in future experiments is planned.