Isobaric studies of the influence of uniaxial pressure on the transitions of pure TGSe crystals for the three directions x, y, z (a * , b, c) are reported. The critical exponents, β, δ and γ , from dielectric constant and hysteresis loop measurements, as well as the coefficients ξ and ζ of the fourth and sixth powers of P in the free-energy expansion under uniaxial pressure were determined. It has been found that uniaxial pressure applied along the a * -axis keeps the transition near a tricritical point for 0 < X < 200 bar, but that when it is applied along the band c-axes it strengthens the second-order phase transition behaviour. The tricritical behaviour of TGSe crystals is discussed and a possible driving mechanism for the change in order of the phase transition is proposed. † We are not concerned here with ferroelastic crystals, for which several examples of a TCP or Lifshitz TCP (LTCP) are known and have been studied both experimentally and theoretically.