General interpolating expressions, valid for near- and arbitrary overcritical sizes of clusters, are proposed for the nucleation fluxes and distributions. Results are expressed in terms of the deterministic growth rates, and are characterized by a non-Gaussian dependence on the size of nuclei. In a sense, the proposed approximations combine the positive aspects of the parabolic model by Trinkaus and Yoo [Philos. Mag. A 55, 269 (1987)] and of the boundary layer ("matched asymptotic") solution earlier described by the author [Sov. Phys. Tech. Phys. 32, 76 (1987); 33, 1338 (1988)]. Specifications of the general results are made for several mainstream nucleation models via selection of appropriate growth rates. Examples include surface- and diffusion-limited nucleation in the continuous (Zeldovich-Frenkel) and discrete (Becker-Doring, Turnbull-Fisher) versions of the nucleation equation.