We perform fits of unconventional dark energy models to the available data from high-redshift supernovae, distant galaxies and baryon oscillations. The models are based either on brane cosmologies or on Liouville strings in which a relaxation dark energy is provided by a rolling dilaton field (Q-cosmology). An interesting feature of such cosmologies is the possibility of effective four-dimensional negative-energy dust and/or exotic scaling of dark matter. An important constraint that can discriminate among models is the evolution of the Hubble parameter as a function of the redshift, H(z). We perform fits using a unifying formula for the evolution of H(z), applicable to different models. We find evidence for a negative-energy dust at the current era, as well as for exotic-scaling (a^{-delta}) contributions to the energy density, with 3.3