We utilize the band structure of a mesoscopic Josephson junction to construct low noise amplifiers. By taking advantage of the quantum dynamics of a Josephson junction, i.e. the interplay of interlevel transitions and the Coulomb blockade of Cooper pairs, we create transistor-like devices, Bloch oscillating transistors, with considerable current gain and high input impedance. In these transistors, correlated supercurrent of Cooper pairs is controlled by a small base current made of single electrons. Our devices reach current and power gains on the order of 30 and 5, respectively. The noise temperature is estimated to be around 1 Kelvin, but it is realistic to achieve TN < 0.1 Kelvin. These devices provide quantum-electronic building blocks that will be useful in low-noise, intermediate-impedance-level circuit applications at low temperatures.