Expressions are summarized for a sample of propagation effects when the refractive index fluctuations deviate from Kolmogorov statistics but are described by a spectrum with a general power law. These effects include a representative amplitude effect, the log amplitude variance, and a phase effect, the coherence length. The expressions provide the numerical coefficients, wavelength dependence and path weighting in terms of the power law exponent. The numerical coefficient relating the structure function and the spectrum is also given in terms of the arbitrary power law exponent. In all these cases, the range of power laws where the relations are valid is explicitly stated. The methodology is also extended to the case of finite outer scale. The techniques can be readily extended to other propagation effects and presents a formalism for evaluating the importance to propagation of deviations from Kolmogorov statistics.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.