Some insights into the method of center projection

We present several new results which pertain to the successes of center pro jection in maximal center gauge (MCG). In particular, we show why any cente r vortex, inserted "by hand" into a thermalized lattice configuration, will be among the set of vortices found by the center projection procedure. We show that this "vortex-finding property" is lost when gauge-field configura tions are fixed to Landau gauge prior to the maximal center gauge fixing; t his fact accounts for the loss of center dominance in the corresponding pro jected configurations. Variants of maximal center (adjoint Landau) gauge ar e proposed which correctly identify relevant center vortices.