We present results of Monte Carlo simulations of partially ionized polyelectrolytes where the charged beads interact through screened Coulomb potentials of Debye-Huckel form. We discuss the behavior of the mean square end-to-end distance versus chain length for a variety of degrees of ionization and added salt concentrations, including the dependence of the apparent scaling exponent on the degree of ionization. We also present estimates for the infinite-chain persistence length, obtained both directly from finite-chain results and by extrapolation from the distribution of bond angles relative to the central bond.