A superconducting transistor structure comprising two Josephson tunnel junctions connected in series and a small island in between, which is capacitively coupled to a gate, is considered. When self-capacitances of the junctions are sufficiently small that the corresponding charging energy E_c is of the order of magnitude of the Josephson coupling strength E_J (and both are ≫k_BT), the interplay of the charging and Josephson effects in the circuit becomes essential. This leads to a characteristic I-V curve which can be effectively modulated by the gate in two limit cases of external electrodynamic impedance Z_s(ω): (a) Z_s = R_s ≫ R_Q ≈ 6.5 kΩ and (b) R_s ≪ R_Q. Both circuits can serve as electrometers which are competitive with traditional single-electron devices. Preliminary experimental results are discussed.