Little-Higgs corrections to precision data after CERN LEP2

We reconsider little-Higgs corrections to precision data. In five models with global symmetries SU (5), SU (6), SO (9) corrections are (although not explicitly) of ``universal`` type. We get simple expressions for the ^S, ^T, W, Y parameters, which summarize all effects. In all models W, Y0 and in almost all models ^S> (W+Y) /2. Results differ from previous analyses, which are sometimes incomplete, sometimes incorrect, and because we add LEP2 ee cross sections to the data set. Depending on the model, the constraint on f ranges between 2 and 20 TeV. We next study the simplest little-Higgs model (and propose a related model) which is not universal and affects precision data due to the presence of an extra Z^' vector. By restricting the data set to the most accurate leptonic data we show how corrections to precision data generated by a generic Z^' can be encoded in four effective ^S, ^T, W, Y parameters, giving their expressions.