The imaginary-time discretized path integral for systems interacting through Coulomb potentials and/or bounded by hard walls behaves pathologically. In this paper we give an analysis of the pathologies. A new method is used to calculate the path integral for the Coulomb system within the primitive algorithm. This is done by constructing an effective potential that implicitly depends on Trotter number P. The procedure makes possible the treatment of Coulombic potentials by means of Monte Carlo at surprisingly low Trotter numbers and without the need of computing three-body potentials, necessary when high-order approximants for the density matrix are employed.