We will consider minimal subshifts with complexity such that the difference from n to n+1 is constant for all large n and impose one more condition (which we call the Regular Bispecial Condition). The shifts that arise naturally from interval exchange transformations belong to this class. A minimal interval exchange transformation on d intervals has at most d/2 ergodic probability measures. This well-known result was due to Katok and later Veech using symplectic arguments. We work to show this bound by combinatorial means on our more general class of subshifts. This is ongoing work with Michael Damron.