Abstract The IceCube Neutrino Observatory, a cubic kilometer scale Cherenkov detector deployed in the deep ice at the geographic South Pole, investigates extreme astrophysical phenomena by studying the corresponding high-energy neutrino signal. Its discovery of a diffuse flux of astrophysical neutrinos with energies up to the PeV scale in 2013 has triggered a vast effort to identify the mostly unknown sources of these high energy neutrinos. Here, we present a new IceCube point-source search that improves the accuracy of the statistical analysis, especially at energies of a few TeV and below. The new approach is based on multidimensional kernel density estimation for the probability density functions and new estimators for the observables, namely the reconstructed energy and the estimated angular uncertainty on the reconstructed arrival direction. The more accurate analysis provides an improvement in discovery potential up to ∼30% over previous works for hard spectrum sources.