We investigate low-temperature and low-voltage-bias charge transport in a superconducting Al single electron transistor in a dissipating environment, realized as on-chip high-ohmic Cr microstrips. In samples with relatively large charging energy Ec≫EJ, where EJ is the Josephson coupling energy, two transport mechanisms were found to be dominant, both based on discrete tunneling of individual Cooper pairs: Depending on the gate voltage Vg, either sequential tunneling of pairs via the transistor island [in the conducting state of the transistor around the points Qg≡CgVg=e mod (2e), where Cg is the gate capacitance] or their cotunneling through the transistor (for Qg away of these points) was found to prevail in the net current. As the conducting state of our transistors had been found to be subject to quasiparticle poisoning, high-frequency gate cycling (at f∼1 MHz) was applied to study the sequential tunneling mechanism. A simple model based on the master equation was found to be in a good agreement with the experimental data. © 2004 American Institute of Physics.