A new method for the retrieval of the spectral refractive indices of micrometer-sized particles from infrared aerosol extinction spectra has been developed. With this method we use a classical damped harmonic-oscillator model of molecular absorption in conjunction with Mie scattering to model extinction spectra, which we then fit to the measurements using a numerical optimal estimation algorithm. The main advantage of this method over the more traditional Kramers-Kronig approach is that it allows the full complex refractive-index spectra, along with the parameters of the particle size distribution, to be retrieved from a single extinction spectrum. The retrieval scheme has been extensively characterized and has been found to provide refractive indices with a maximum uncertainty of approximately 10% (with a minimum of approximately 0.1%). Comparison of refractive indices calculated from measurements of a ternary solution of HNO3, H2SO4, and H2O with those published in J. Phys. Chem. A 104, 783 (2000) show similar differences as found by other authors.