The magnetic-field dependence of the critical current I-c(H) is consid
ered for a short Josephson junction with the critical current density
j(c) alternating along the tunnel contact. Two model cases, periodic a
nd randomly alternating j(c), are treated in detail. Recent experiment
al data on I-c(H) for grain-boundary Josephson junctions in YBa2Cu3Ox
are discussed.