We investigated the current carrying capacities of ten NbTi superconductors having a CuNi matrix with diameters between 50 and 300 ¿m as function of an applied magnetic field of 0 to 6 tesla. The effects of the method of wire fixation and the electrical connections were studied. The results are compared to those obtained with two common conductors with Cu matrix. We observed large differences of a factor 2 between the critical current densities of the various CuNi matrix conductors. Furthermore, it is remarkable that the best CuNi matrix conductors have critical current densities which are much higher than those in Cu matrix conductors.