We present a technique to detect Ultra-Faint Dwarf Galaxies (UFDs) in the Galactic Halo, using sky and proper motion information.The method uses wavelet transforms to detect peaks in the sky and proper motion planes, and to evaluate the probability of these being stochastic fluctuations. We aim to map thoroughly the detection limits of this technique. For this, we have produced a library of 15,000 synthetic UFDs, embedded in the Gaia Universe Model Snapshot (GUMS) background (Robin et al. 2012), each at a different distance, different luminosity, half-light radius, velocity dispersion and center-of-mass velocity, varying in ranges that extend well beyond those spanned by known classical and ultra-faint dSphs. We use these synthetic UFDs as a benchmark to characterize the completeness and detection limits of our technique, and present our results as a function of different physical and observable parameters of the UFDs (see full poster for more details at https://gaia.ub.edu/Twiki/pub/GREATITNFC/ProgramFinalconference/Poster_UFGX_Bcn_C_Mateu.pdf).