We present experimental data for the Pm3m-I4/mcm phase transitions in the perovskite crystals KMn1-xCaxF3 and SrTiO3. Comparison of calorimetric data (latent heat and specific heat) with order parameter data (measured with X-ray rocking methods) indicates that these transitions follow mean-field behaviour, and may be described using Landau potentials where the free energy expansion includes terms up to Q
6. This potential is characteristic of transitions close to the tricritical point. Comparison of the behaviour of SrTiO3 and KMnF3 indicates that KMnF3 is closer to the tricritical point; a small amount of substitution of Ca for Mn causes the transition to cross the tricritical point from first order to second order behaviour.