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) over cap,(T) over cap ,W,Y parameters, which summarize all effects. In all models W,Y >= 0 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 e (e) over bar -> f (f) over bar 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) over cap,(T) over cap ,W,Y parameters, giving their expressions.