We present a detailed analysis on nonstandard neutrino interactions (NSI) with electrons including all muon and electron (anti)-neutrino data from existing accelerators and reactors, in conjunction with the 'neutrino counting' data (e{sup +}e{sup -}{yields}{nu}{nu}{gamma}) from the four LEP collaborations. First we perform a one-parameter-at-a-time analysis, showing how most constraints improve with respect to previous results reported in the literature. We also present more robust results where the NSI parameters are allowed to vary freely in the analysis. We show the importance of combining LEP data with the other experiments in removing degeneracies in the global analysis constraining flavor-conserving NSI parameters which, at 90% and 95% C.L., must lie within unique allowed regions. Despite such improved constraints, there is still substantial room for improvement, posing a big challenge for upcoming experiments.