The maximum zero-voltage tunnel current I
0and its fluctuations were measured for Josephson tunnel junctions as a function of the normal state resistance

in the range of 50-300 Ω at

K. The junctions, based on pure lead, have areas of about 100 µm
2, corresponding to capacitances

of about 3 pF. The results obtained from a simple noise model, describing the junction in the zero-voltage state as a parallel resonant circuit with parameters

, and

, are in good agreement with the experiments. It is shown that the deviation of the experimental results for high-resistivity junctions from the theory of Ambegaokar and Baratoff is due to thermal noise currents originating in the normal state resistance

.