We consider three methods for determining neutron nonelastic cross sections: direct measurement by transmission of neutrons through a spherical shell; subtraction of the angle-integrated elastic cross section from the total cross section; and a modification of the subtraction technique using Wick’s limit that in favorable cases can significantly reduce the errors in the subtraction method. We show new results using the modified subtraction technique for nonelastic cross sections at 21.6 MeV neutron energy over a wide mass range, and discuss criteria that should be satisfied in order for the modified subtraction technique to be reliable.