Strong Mie scattering signatures hamper the chemical interpretation and multivariate analysis of the infrared microscopy spectra of single cells and tissues. During recent years, several numerical Mie scatter correction algorithms for the infrared spectroscopy of single cells have been published. In the paper at hand, we critically reviewed existing algorithms for the correction of Mie scattering and suggest improvements. We developed an iterative algorithm based on Extended Multiplicative Scatter Correction (EMSC), for the retrieval of pure absorbance spectra from highly distorted infrared spectra of single cells. The new algorithm uses the van de Hulst approximation formula for the extinction efficiency employing a complex refractive index. The iterative algorithm involves the establishment of an EMSC meta-model. While existing iterative algorithms for the correction of resonant Mie scattering employ three independent parameters for establishing a meta-model, we could decrease the number of parameters from three to two independent parameters, which reduced the calculation time for the Mie scattering curves for the iterative EMSC meta-model by a factor of 10. Moreover, by employing the Hilbert transform for evaluating the Kramers–Kronig relations based on a FFT algorithm in Matlab, we further improved the speed of the algorithm by a factor of 100. For testing the algorithm we simulate distorted apparent absorbance spectra by utilizing the exact theory for the scattering of infrared light at absorbing spheres, taking into account the high numerical aperture of infrared microscopes employed for the analysis of single cells and tissues. In addition, the algorithm was applied to measured absorbance spectra of single lung cancer cells.