The four-terminal short sample test used to measure the critical currents of commercial superconducting composites typically employs equivalent electric field levels of 10(-5) and 10(-4) Vm-1 to specify the onset of the superconducting-resistive transition. We describe refinements to this technique enabling resolution of the transition at the 10(-7) Vm-1 level. Data on four samples of NbTi conductor are compared over the full electric field range available using the above method, illustrating the influence of composite geometry and matrix material on the detailed form of the E-J characteristic.