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 theŜ,T , W, Y parameters, which summarize all effects. In all models W, Y ≥ 0 and in almost all modelsŜ > (W + Y )/2. Results differ from previous analyses, which are sometimes incomplete, sometimes incorrect, and because we add LEP2 eē → ff 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 effectiveŜ,T , W, Y parameters, giving their expressions.