We describe a simple method for determining the neutron-absorption cross sections of radioactive nuclides and its application to 22Na and 126I. These nuclides are produced by fast-neutron reactions in cadmium-wrapped and unshielded samples simultaneously irradiated with cobalt flux wires. Values for the thermal cross section, σ0, the resonance integral, Σ′, and s0 are calculated from the data using the Westcott convention. The results are as follows: for 22Na, σ0 = (5.11 ± 0.31) × 104 b, s0 = 2.3 ± 0.1, and Σ′ = (1.0 ± 0.1) × 105 b; for 126I, σ0 = (9.0 ± 5.0) × 103 b.