The ground state of an N-monomer charged polymer, in the absence of screeni
ng, is stretched, with nonextensive energy growing as N lnN. If the allowed
bond angles are discrete, only discrete changes in conformation are possib
le, and the elementary excitations have energy growing as lnN. Using analyt
ical arguments, and Monte Carlo simulations, we show that such a polymer is
rigid (flat) at low temperature T, and flexible (rough) at high T. The rou
ghness exponent, for the scaling of transverse fluctuations with N, varies
continuously with T, reaching the value for models which permit continuous
changes in geometry only at very high T.