Current-voltage, I(V), and current-magnetic field, I(h), characteristics of a short molecular wire are studied in the framework of a model which accounts for strong Coulomb repulsion between the transferred electrons. The given approach avoids the fact that statistically the wire simultaneously transmits more than a single excess electron. First, we address short molecular wire systems which exhibit a narrow peak in the I(V)-characteristics. Recent experimental data of the peak current are well reproduced by our theory. In a second part, we study wires which contain paramagnetic ions mediating the ET. With the focus being on the low-temperature region, a step-like behavior of the current versus the magnetic field is predicted.