  We consider some applications of the Renormalization Group flow equations
obtained by resorting to a specific class of proper time regulators. Within
this class a particular limit that corresponds to a sharpening of the effective
width of the regulator is investigated and a procedure to analytically
implement this limit on the flow equations is shown. We focus on the critical
exponents determination for the O(N) symmetric scalar theory in three
dimensions. The large N limit and some perturbative features in four dimensions
are also analysed. In all problems examined the results are optimized when the
mentioned limit of the proper time regulator is taken.
