The possibility of unifying dark matter and dark energy has recently attracted considerable interest. In this so called quartessence scenario, a single component is responsible for both the clustering of matter and the accelerated expansion of the universe. A model archetype for such scenario is provided by the Chaplygin gas. Although this model is in agreement with the data on the expansion history, problems arise in the power spectrum of density fluctuations for adiabatic perturbations. In this contribution we consider other quartessence models and confirm that instabilities and oscillations in the matter power spectrum are a characteristic of more generic quartessence models, namely those with a convex equation of state. We show that, as in the Chaplygin case, this kind of problem can be solved by considering intrinsic non-adiabatic perturbations such that, as an initial condition, the perturbed fluid is gradient pressure free. We also discuss how the problems of adiabatic quartessence can be circumvented by other types of equations of state.