The tunneling Hamiltonian formalism is applied to calculate the tunneling currents through a small superconducting tunnel junction. The formalism is extended to nonconstant tunneling matrix elements. The electrodes of the junction are assumed to consist of high critical temperature superconductors. They are described by a BCS-type model with anisotropic gap parameter Delta k, to account for the high anisotropy observed in these materials. The numerical computation of the tunneling currents reveals new qualitative features which could explain many puzzling questions arising from recent experimental results.