  We perform a one-loop analysis of the rho parameter in the Littlest Higgs
model, including the logarithmically enhanced contributions from both fermion
and scalar loops. We find the one-loop contributions are comparable to the tree
level corrections in some regions of parameter space. The fermion loop
contribution dominates in the low cutoff scale f region. On the other hand, the
scalar loop contribution dominates in the high cutoff scale f region and it
grows with the cutoff scale f. This in turn implies an upper bound on the
cutoff scale. A low cutoff scale is allowed for a non-zero triplet VEV.
Constraints on various other parameters in the model are also discussed. The
role of triplet scalars in constructing a consistent renormalization scheme is
emphasized.
