We have studied the parametric amplification properties of an internally pumped Josephson tunnel junction, where the shunt contained resistive and inductive components. The amplification was, in this case, limited by circuit component values to less than 8 dB at 10 GHz, but it was very stable against variations in bias conditions. The amplifier gain‐bandwidth product was large and the noise level very low. We estimated the noise temperature to be less than 50 K, which should make the device attractive for mm‐wave amplification.