An investigation into the bistability of positively curved laminated composite slit tubes is presented, establishing a natural extension in this area which has previously been focused on straight tubes. Curved slit tubes are modeled as the surface segments of a torus. The design space is explored through a parametric study to investigate the effect on the second stable state, representing a small coil. This includes the effects of longitudinal curvature, cross-section subtending angles, non-uniform transverse curvature and spatially varying laminate properties. The second equilibrium state is determined through strain energy minimization using the Rayleigh-Ritz method. To verify the model, samples were manufactured from glass-fiber braid and polypropyleneresin. This investigation finds: (i) the initial curvature along the length of the tube has little effect on coil radius, however, the coil has a distinct barrel shape; (ii) highly enclosed and (iii) highly curved cross-sections result in higher edge strains of the second equilibrium, enabling identification of practical bistable tubes, and conversely; (iv) the greater the initial curvature along the length of the tube, the lower the second equilibrium strain.