We have performed a comparison of ten models that predict the temporal behavior of laser-induced incandescence (LII) of soot. In this paper we present a summary of the models and comparisons of calculated temperatures, diameters, signals, and energy-balance terms. The models were run assuming laser heating at 532 nm at fluences of 0.05 and 0.70 J/cm2 with a laser temporal profile provided. Calculations were performed for a single primary particle with a diameter of 30 nm at an ambient temperature of 1800 K and pressure of 1 bar. Preliminary calculations were performed with a fully constrained model. The comparison of unconstrained models demonstrates a wide spread in calculated LII signals. Many of the differences can be attributed to the values of a few important parameters, such as the refractive index function E(m) and thermal and mass accommodation coefficients. Constraining these parameters brings most of the models into much better agreement with each other, particularly for the low-fluence case. Agreement among models is not as good for the high-fluence case, even when selected parameters are constrained. The reason for greater variability in model results at high fluence appears to be related to solution approaches to mass and heat loss by sublimation.