Superconducting critical current densities Jc of pure and alloyed Nb3Sn layers of bronze processed monofilamentary wires were measured at 1.8 and 4.2 K in magnetic fields up to 24 T. The maximum in Jc at 20 T was found for Nb3Sn layers which were fabricated using (Nb ∼3.3 at. % Ti) cores, and the values of Jc were ∼670 and ∼370 A/mm2 at 1.8 and 4.2 K, respectively. These values are ∼5 and ∼25 times greater than those for ‘‘pure’’ Nb3Sn wires at these same temperatures. The functional dependence of Jc on the Ti content was also identical to that for the measured values of Hc2 vs Ti content for these wires. The maximum value of Hc2 of the wires with the matrix in place was 26.3 T for the wire which was fabricated from the core containing 3.3 at. % Ti in Nb.