  Using a grid of $\sim 2$ million elements ($\Delta z = 0.005$) adapted from
COSMOS photometric redshift (photo-z) searches, we investigate the general
properties of template-based photo-z likelihood surfaces. We find these
surfaces are filled with numerous local minima and large degeneracies that
generally confound rapid but "greedy" optimization schemes, even with
additional stochastic sampling methods. In order to robustly and efficiently
explore these surfaces, we develop BAD-Z [Brisk Annealing-Driven Redshifts
(Z)], which combines ensemble Markov Chain Monte Carlo (MCMC) sampling with
simulated annealing to sample arbitrarily large, pre-generated grids in
approximately constant time. Using a mock catalog of 384,662 objects, we show
BAD-Z samples $\sim 40$ times more efficiently compared to a brute-force
counterpart while maintaining similar levels of accuracy. Our results represent
first steps toward designing template-fitting photo-z approaches limited mainly
by memory constraints rather than computation time.
