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 Q6. 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.