/ AbstractPhonon-mediated cryogenic calorimeters find application in rare event searches due to their intrinsically low energy threshold. Achieving the best sensitivity for this kind of detectors is crucial for signal identification, leading to various optimization techniques. In this work, we present two complementary methods to increase the sensitivity of cryogenic detectors read out by transition-edge sensors, developed and tested in the context of the NUCLEUS experiment. The first procedure maps the signal-to-noise ratio of the device across a wide range of operating points, to identify the configuration with maximal sensitivity to be used during data taking. The second method exploits the double readout of the detector, combining the information on different channels with a two-dimensional optimum filter analysis that effectively lowers the energy threshold. With both techniques at the same time, we obtained a baseline resolution of 2.94 $\pm$ 0.05 (stat) eV using a CaWO4 based detector, achieving a promising result in view of the first run of NUCLEUS at the experimental site.