The configurational properties of strongly charged polyelectrolytes accompanied by neutralizing counterions in dilute solutions are simulated using the cooperative motion algorithm on the face-centered-cubic lattice. The full Coulomb potential and the excluded volume condition between different ions/beads are taken into account and the reduced temperature T-* is considered the main, variable parameter. The calculations that have been carried out for solutions of both single and several chains indicate a few regions of their behavior: (1) for T-*-->infinity, it corresponds to that of neutral, self-avoiding polymers under good solvent conditions; (2) for T(*)approximate to1, due to the electrostatic interactions being effectively stronger, the chains are more outstretched compared to their size at other temperatures; (3) for T-* well below one, the counterion condensation becomes more and more dominant, which gradually leads to strongly collapsed chains; and (4) at the lowest temperatures the chains and counterions assume low-energy configurations in the form of neutral, compact aggregates. (C) 2004 American Institute of Physics.