Quasi-wavelet (QW) representations of turbulence are composed of self-similar, eddy-like structures. Although the QW functions are localized in both the spatial and spectral domains, they are not true wavelets in the sense that they do not form a complete basis or have zero mean. Nonetheless, they appear to be very useful for applications such as wave scattering and structural wind loading. In this paper, the formulation of the isotropic QW model is presented. An equation relating the energy spectrum of the turbulence to the envelope function of the quasi-wavelets (eddies) is derived. From this equation, a unique eddy envelope corresponding to the von Kármán energy spectrum is determined. Many other possible eddy envelope functions, including exponential and Gaussian eddies, yield energy spectra highly similar to the von Kármán spectrum. The generalized spectral equation proposed by L. Kristensen et al (Boundary-Layer Meteor. 47, 149–193, 1989) is found to yield divergent eddy envelopes for many choices of parameters, including the special case of the Kansas-type empirical spectrum (J. C. Kaimal et al, Quart. J. Roy. Meteorol. Soc. 98, 563–589, 1972). This behavior suggests that many empirical spectra can be justified only on the basis of turbulence anisotropy. This material is partly based upon work that was supported by the U.S. Army Research Office under contract number DAAD19-01-1-0640 (administered by W. Bach).