We describe an approach to the experimental determination of the critical micelle concentration (CMC) in solutions of uncharged micelles by the analysis of small-angle neutron scattering data. It is shown that, in dilute solutions, the dependence of the product of forward scattering intensity and apparent squared radius of gyration is a linear function of the total surfactant concentration. The ratio of the two parameters of this function gives the concentration of surfactant in a monomeric state, which can be used as a reliable estimate of CMC. In the case under investigation (AOT + X . H2O + C6D6) at X = 0 we found CMC = 0.80 +/- 0.04 mM, which is in reasonable agreement with the values reported by the other authors. Our first experiments at X = 4.3 and X = 8.6 show CMC = 2.2 +/- 1.0 mM and 1.5 +/- 0.6 mM, respectively. It seems plausible that the addition of water does not cause any serious diminution of the CMC in this system.