Fluctuations of order parameters Q near a tricritical point coupled with strain e( varies as eQ²) lead to fluctuation-induced first-order phase transitions. Anisotropic fluctuations with strong correlations along a 'hard' direction show a much reduced first-order behaviour. In the case of improper ferroelastics the fluctuation-related renormalizations become immeasurably small and a classic tricritical behaviour is expected. Experimental observations of such fluctuations are facilitated if the fluctuating order parameter couples bi-quadratically with a second, non-critical order parameter which is used as tracer. The fluctuation-induced renormalization of the tracer order parameter is calculated.