Several time-independent methods have been devised for measuring the phase gamma of the Cabibbo-Kobayashi-Maskawa unitarity triangle. It is shown that such measurements generally suffer from discrete ambiguity which is at least 8-fold, not 4-fold as commonly stated. This has serious experimental implications, which are explored in methods involving B->DK decays. The measurement sensitivity and new physics discovery potential are estimated using a full Monte Carlo detector simulation with realistic background estimates.