Lee and Stroud (1992) have predicted that the critical current I c(B) in a composite superconducting material should display a constant Value in moderately high magnetic fields, giving rise to a 'plateau region'. Critical current measurements on granular metallic Al-Ge films, located considerably above the metal-insulator transition (MIT), display well defined plateaus. And these measurements confirm most of the Lee-Stroud predictions. In contrast, films located just above the MIT exhibit continuously decreasing critical currents with increasing magnetic fields. These results are explained using a tunnelling junction model proposed by Peterson and Ekin and extended by Papa and Altshuler. From the fitting results, a simple picture. Involving both models, emerges. Which explains the behaviour of Ic versus magnetic field in pressed powdered YBCO samples and in Ag-sheathed Bi-based HTC wires, as well as in the Al-Ge films.