A semi-analytical version of single-angle ellipsometric inversion to determine the refractive index of non-absorbing films is re-examined to explore the possibility of speeding up and enhancing the reliability of its computational implementation by an a priori rejection of one of two potential solutions propagated from the one of the two roots of the quadratic equation arisen in the inversion process. The distribution of solution-determining parameters and root selection over the (refractive index)-thickness solution space depending on the measurement variables of wavelength and angle of incidence is surveyed and exhibits an interesting pattern, which can be harnessed depending on materials. Optimization depending on the measurement variables and potential application in spectroscopic and in situ ellipsometry is discussed. The feasibility of the method has been tested with samples of aluminium oxide and titanium oxide films on silicon substrates.