Particle composition and size distribution impact the magnitude and spectral shape of absorption and backscattering, the inherent optical properties that determine remote sensing reflectance. Roesler \& Perry (1995) proposed an inversion model that derives spectral absorption and backscattering coefficients from spectral reflectance measurements. In its original form, this model used assigned spectral shapes, chosen to be broadly representative, for each component of absorption and backscattering, and derived the magnitude of each component via a non-linear least squares regression. However, we know that there is variability in the actual spectral shapes of the components, and that we can gain a better understanding of particle characteristics by examining that variability. In this study, we explore the possibility of allowing spectral shapes, as well as component magnitudes, to vary within the solution to the model. Tripton and gelbstoff absorption are modeled as exponential functions of wavelength, and particle backscattering as a hyperbolic function, all with variable spectral slopes. We test this model with measurements of remote sensing reflectance (PRR, Biospherical), absorption and attenuation (ac9, WETLabs), and backscattering (Hydroscat 6, Hobilabs) in the Damriscotta River, Maine during August 2001. As expected, interactions occur among components with similar spectral shapes and the model is unstable if all of the terms are allowed to vary simultaneously. However, if certain subsets of terms are allowed to vary, absorption and backscattering components are well reproduced. Individual components are best reproduced using particular subsets of variables. Our results suggest that allowing some constrained variation in spectral shape within the model can produce component spectra that are representative of specific particle populations. This derivation of absorption and backscattering spectra can provide a mechanism for obtaining more detailed information regarding particle composition and size distribution from reflectance data.