Little-Higgs corrections to precision data after 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 Shat, That, W, Y parameters, which summarize all effects. In all models Shat > (W+Y)/2 and That, W, Y\ge 0. Results differ from previous analyses, which are sometimes incomplete, sometimes incorrect, and because we add LEP2 e ebar --> f fbar 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 new 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 Shat, That, W, Y parameters, giving their expressions.