Interplanetary Laser Ranging (ILR) is an experimental satellite navigation technique with the potential to produce cm- to mm-level accurate and precise range observations over interplanetary distances. This is an improvement over current radio ranging techniques, which can achieve m-level performance. One common application of navigation data is the estimation of physical and astronomical parameters. To utilize the improved observation quality of ILR, it is necessary to use sufficiently detailed observation- and dynamical models during parameter estimation. We investigate the influence of relativistic modelling on parameter estimation quality using ILR data. Simulated parameter estimation experiments involving a Juno-like Jovian orbiter were used to gauge the impact of 22 different relativistic effects. The spacecraft's initial state, the mass of Jupiter and two post-Newtonian parameters were estimated in each experiment. Parameter estimation error, observation errors and estimation residuals were used as metrics to quantify the influence of each effect. Rough preliminary estimates of an effect's magnitude were found to be a good predictor of the actual impact on estimation error, with some exceptions. Excluding the gravitational influence of Jupiter's velocity and the Jupiter-Sun coupled gravity resulted in almost no change in estimation error, likely due to compensation by the Newtonian gravity term. Similar compensatory relationships can be identified by comparing mean observation errors with mean estimation residuals. Including empirical accelerations in the estimation process reduces the impact of these outliers.