NASA's Mars Science Laboratory rover Curiosity (MSL) has measured simultaneous fluctuations in wind and atmospheric pressure caused by passing convective vortices, i.e. dustless dust devils. We study the dynamics of these vortices by fitting a mathematical vortex model to the wind and pressure measurements of MSL. The model matches the data adequately well in 29 out of the 33 studied vortex pass events having sufficient data quality. Clockwise and counterclockwise rotating directions are equally common among the studied convective vortices. The vortices seem to prefer certain trajectories, e.g. avoiding steep slopes. However, our results show that due to sensitivity constraints of the method, central pressure drops of Martian dust devils can usually not be accurately determined by fitting a theoretical vortex model to simultaneous pressure and wind measurements of a single station. We also present a methodology extension for further constraining the trajectories and the strengths of dust laden vortices (i.e. dust devils), based on concurrent in-situ solar irradiance measurements. We apply this methodology to the only evidently dust laden vortex in our data set and show that its dust lifting capacity is probably based not only on wind stress lifting.