Superconducting Bi-2212/Ag monocore wires of 0.65, 1.0, 1.2 and 1.5 mm diameter have been fabricated by the powder-in-tube method. The critical current densities increase with decreasing wire diameters. For short specimens of 0.65 mm diameter, maximum critical current densities of up to 120 000 A cm(-2) (B = 0) and 40 000 A cm(-2) (B = 12T) have been achieved at 4.2 K. For wires of 1.5 mm diameter the scatter in critical current data is approximate to 10% within groups of specimens heat treated together. For the thinner wires this scatter is more pronounced. The heat treatment conditions leading to the highest critical current densities have been found to depend on the wire diameter. An increasing thickness of the silver sheath may be responsible for a retarded release of oxygen from the core before the superconductor is partially molten. Evidence for grain alignment in a thin layer at the interface to the silver of typically 10-20 mu m thickness has been found by scanning electron microscopy. A model which explains the observed scaling behaviour of the critical current density with the wi re diameter has been developed. Using this model the critical current density in the interfacial region can be estimated.