In the late 1950s, Convair began working on a new model of the B-58, known as B-J/58 by the company and unofficially as the B-58C by the USAF. The B-58C incorporated significant airframe modifications, including a new wing leading edge, a larger tail area, a 5-foot fuselage extension. Power was to be provided by four Pratt & Whitney J58 turbojets, each offering a thrust of 32,500 lb.s.t. The aircraft was envisaged by Convair as a lower-cost alternative to the North American B-70 Valkyrie. The C-model had an estimated top speed approaching Mach 3, a supersonic cruise capability of approximately Mach 2, plus a service ceiling of about 70,000 feet.
However, the USAF deemed that the B-58C was too heavily-based on an older configuration and lacked the growth potential of the B-70. The ARDC concluded that Convair's estimate of a 5200-nautical mile unrefuelled range for the B-58C was grossly overoptimistic. In addition, the extensive use of aluminum in the structure would probably result in problems with the overheating produced by prolonged high-speed flight. Furthermore, in early 1961, the new Kennedy administration was having second thoughts about the B-70 project itself and had canceled production, reducing the program to only three experimental aircraft. Consequently, the Air Staff and SAC did not want to risk the financial interference of a new project. In April of 1961, Convair was informed by the USAF that they had no further interest in the B-58C, and further work on the project was abandoned.