A fast transition between a standard matter-like era and a late Λcold dark matter (ΛCDM)-like epoch (or more in general, a CDM+DE era), generated by a single unified dark matter (UDM) component, can provide a new interesting paradigm in the context of general relativity, alternative to ΛCDM itself or other forms of dark energy (DE) or modified gravity theories invoked to explain the observed acceleration of the Universe. UDM models with a fast transition have interesting features, leading to measurable predictions, thus they should be clearly distinguishable from ΛCDM (and alternatives) through observations. Here, we look at different ways of prescribing phenomenological UDM models with fast transition, then focusing on a particularly simple model. We analyse the viability of this model by studying features of the background model and properties of the adiabatic UDM perturbations, which depend on the effective speed of sound and the functional form of the Jeans scale. As a result, theoretical constraints on the parameters of the models are found that allow for a behaviour compatible with observations.