  We calculate the tree-level electroweak precision constraints on a wide class
of little Higgs models including: variations of the Littlest Higgs SU(5)/SO(5),
SU(6)/Sp(6), and SU(4)^4/SU(3)^4. By performing a global fit to the precision
data we find that for generic regions of the parameter space the bound on the
symmetry breaking scale f is several TeV, where we have kept the normalization
of f constant in the different models. For example, the ``minimal''
implementation of SU(6)/Sp(6) is bounded by f>3.0 TeV throughout most of the
parameter space, and SU(4)^4/SU(3)^4 is bounded by f^2 = f_1^2+f_2^2 > (4.2
TeV)^2. In certain models, such as SU(4)^4/SU(3)^4, a large f does not directly
imply a large amount of fine tuning since the heavy fermion masses that
contribute to the Higgs mass can be lowered below f for a carefully chosen set
of parameters. We also find that for certain models (or variations) there exist
regions of parameter space in which the bound on f can be lowered into the
range 1-2 TeV. These regions are typically characterized by a small mixing
between heavy and standard model gauge bosons, and a small (or vanishing)
coupling between heavy U(1) gauge bosons and the light fermions. Whether such a
region of parameter space is natural or not is ultimately contingent on the UV
completion.
