We present in this paper a solution to drastically improve the deformation time-series retrieval capability of the small baseline differential SAR interferometry (DInSAR) processing chain based on the cascade of the extended minimum cost flow (EMCF) phase unwrapping method and of the small baseline subset (SBAS) inversion technique. This improvement relies on the inclusion of two preprocessing steps implementing an effective noise-filtering operation and an efficient interferogram selection procedure, respectively. The former step filters out the noise affecting the phase components of a redundant set of conventional multi-look small baseline interferograms. This is achieved by solving, for each pixel, a nonlinear minimization problem based on computing the wrapped phase vector that minimizes the weighted circular variance of the phase difference between the original and noise-filtered interferograms. This technique is very easy to implement because it does not require any pixel selection step to be applied to the exploited full-resolution SAR images, and it has no need of any a priori information on the statistics of the complex-valued SAR images. The latter step, implementing the interferogram selection procedure, is carried out via a computationally efficient simulated annealing algorithm and allows identifying the optimum set of previously filtered small baseline interferograms to be used as input for the original EMCF-SBAS processing chain by maximizing the (average) coherence values. The presented results, achieved by processing three data sets collected by the ENVISAT ASAR sensor over the Abruzzi region (Central Italy), Mt. Etna volcano (South Italy), and Yellowstone Caldera (WY, USA), demonstrate the effectiveness of the proposed advanced EMCF-SBAS processing chain.