  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.
