The Stratospheric Aerosols and Gas Experiment (SAGE) III instrument onboard the International Space Station (ISS) provides measurements of aerosol extinction, giving information about the aerosol optical properties. Information about the physical properties, which are useful for characterizing aerosols and understanding the chemical processes occurring in the atmosphere, can be obtained from the size distributions of these aerosols that are related to the measured extinction. The use of the Levenberg-Marquardt method is explored to retrieve single mode volume size distributions of stratospheric aerosols from SAGE III/ISS extinction measurements with the goal of determining the viability of the technique. The retrieved size distributions are assumed to be lognormal, and stratospheric aerosols, which are mostly composed of sulfuric acid, are assumed to be spherical with an index of refraction of 1.45. Six of the nine SAGE III/ISS extinction wavelengths are used to obtain the volume density, median radius, and standard deviation that make up the distributions. These distributions are observed under background conditions and after events such as strong wildfires or volcanic eruptions that were able to inject aerosols into the stratosphere. Extinction calculated with the resulting size distributions largely fall within the uncertainty of the measured extinction, and comparisons made with coincident Optical Particle Counter (OPC) balloon measurements from the University of Wyoming in Laramie, Wyoming help to give confidence to the technique.