A fabrication technique for Nb‐Al2O3‐Nb Josephson tunnel junctions is described that is an alternative to the trilayer method generally used. At 4.2 K the magnitude of the low‐frequency noise in the critical currentI0of four junctions with areasAranging from 7.8 to 115 &mgr;m2was characterized byS1/2I0A1/2/I0=(14±6)pA &mgr;m/&mgr;A Hz1/2, whereSI0is the spectral density of the excess noise at 1 Hz. The noise power spectrum of one 3×3 &mgr;m2junction exhibited a Lorentzian feature associated with the emptying and filling of a single trap in the barrier. The low level of noise makes these junctions attractive for use in superconducting quantum interference devices.