Parametric Rietveld refinement is a powerful technique to apply directly physical or empirical equations to the refinement of in situ powder diffraction data. In order to investigate the possibilities and limitations of parametric Rietveld refinements for high pressure data four competitive crystallographic approaches were used to carry out a full structural investigation of the orthoferrite LaFeO 3 (Pbnm at ambient conditions) under high pressure up to 47 GPa. Approach A with traditional Rietveld refinement using atomic coordinates, Approach B where the Rietveld refinement was done by using the rigid body method, Approach C where symmetry modes were used and Approach D where the newly developed method of the rotational symmetry mode description for a rigid body was used. For all approaches sequential as well as parametric refinements were carried out, confirming a second order phase transition of LaFeO 3 to a higher symmetric phase (space group Ibmm) at around 21.1 GPa and an isostructural first order phase transition at around 38 GPa. Limitations due to non-hydrostatic conditions as well as the possibilities of a direct modeling of phase transitions with parametric Rietveld refinement are discussed in detail.