Parametric amplification at 35 GHz has been obtained using a single Josephson tunnel junction as the active element. The amplifier was operated in the singly quasidegenerate mode with a pump frequency at 70 GHz. The noise temperature was measured and found correlated with the gain. At the highest gain achieved, 11.6 dB, the noise temperature was 400 K. The noise temperature was reduced considerably by decreasing the gain. At 8 and 4 dB we found 165±25 K and 50±30 K, respectively. Applied Physics Letters is copyrighted by The American Institute of Physics.