One of the most compelling goals of observational cosmology is the characterisation of the properties of the dark energy component thought to be responsible for the recent acceleration of the universe, including its possible dynamics. In this work we study phenomenological but physically motivated classes of models in which the dark energy equation of state can undergo a rapid transition at low redshifts, perhaps associated with the onset of the acceleration phase itself. Through a standard statistical analysis we have used low-redshift cosmological data, coming from Type Ia supernova and Hubble parameter measurements, to set constraints on the steepness of these possible transitions as well as on the present-day values of the dark energy e...