Free energy for parameterized Polyakov loops in SU(2) and SU(3) lattice gauge theory

We present a study of the free energy of parameterized Polyakov loops P in SU(2) and SU(3) lattice gauge theory as a function of the parameters that characterize P. We explore temperatures below and above the deconfinement transition, and for our highest temperatures T > 5 T_c we compare the free energy to perturbative results.