The problem of UHF propagation is examined for the case of a spherically stratified troposphere having a profile of refractive modulus with a minimum near the surface of the earth. The methods of R. E. Langer are used to develop an asymptotic solution in terms of Whittaker functions, and eigenvalues are determined numerically with a fast computer. The results, which agree with those obtained earlier by other methods, are used to show how the distant field strength varies as the profile changes from a ‘normal’ case to a highly superrefractive case.