Flexible steerable needles can follow complex curved paths inside the human body. In a previous work, we developed a multiple-part steerable needle prototype with a diameter of 1.2 mm, inspired by the ovipositor of parasitoid wasps. The needle consisted of seven nickel-titanium longitudinally aligned wires held together at the tip by a cylindrical ring with seven holes. The steerability of the needle was evaluated in a gelatin phantom and was found to be lower than that of other steerable needles in the literature. One possible cause of this limited steerability is that during motion the wires tend to separate from each other (i.e., bifurcate). Our aim here was to reduce bifurcation in order to increase the steering curvature of the needle, while keeping the diameter around 1.5 mm, and thus compatible with needles used in medical practice. To achieve that, we changed the shape of the ring from cylindrical to conical. We evaluated the steering performance in gelatin, using the conical ring in two configurations: (1) with the apex of the cone towards the needle tip, so that the wires converge, thus expected to reduce bifurcation, (2) with the apex of the cone placed towards the needle base, so that the wires diverge, thus expected to magnify bifurcation. Results showed that the diverging ring generated larger steering curvatures. We can conclude that reducing the bifurcation of the wires is not enough for increasing the steering curvature and that inducing this same phenomenon instead could actually lead to higher curvatures.