The Rayleigh limit of the Lorenz-Mie theory is extended by the Penndorf correction. For the efficiency factors, this extension leads to Qa,s,e<P = Qa,s,eR(1+Πa,s,e) where superscripts P and R denote Penndorf and Rayleigh; subscripts s, a, and e, respectively, scattering absorption, and extinction; and Π the Penndorf correction to the Rayleigh limit. This correction is shown to extend the Rayleigh limit from α ≃ 0.3 to 0.8, α being the particle size parameter. Error contours are generated for the Rayleigh and Penndorf limits for α = 0.3, 0.5, and 0.7 in the 1.5 ⩽ n ⩽ 2.5 and 0.5 ⩽ k ⩽ 1.5 domain which covers the range of soot properties. The practical significance of the Penndorf correction is demonstrated in terms of optical diagnostics and radiative heat transfer. Also, the Planck and Rosseland mean absorption coefficients based on the Penndorf expansion are shown to yield relative to those based on the Rayleigh limit Graphical abstract for this article where subscripts P and R denote the Planck and Rosseland mean absorption coefficients, superscripts P and R denote Penndorf and Rayleigh, Π the Penndorf correction depending on Ms and Ns which are the explicit functions of refractive and absorptive indices of particles, and on the dimensionless number πDTC2 (D being the particle diameter, T the temperature, and C2 the second radiation constant). For larger particles and/or higher temperatures the Penndorf based Planck mean coefficient is shown to deviate considerably from the Rayleigh based Planck mean coefficient. This deviation is exhibited to a somewhat lesser extent by the Penndorf based Rosseland mean coefficient.