  We present a comparative analysis of current observational constraints on
three recently discussed alternative models for explaining the low-redshift
acceleration of the universe: the so-called steady-state torsion model, the
generalized coupling model, and the scale invariant model by Maeder (an example
of a broader class which we also briefly study) These are compared to the
traditional parameterization of Chevallier, Polarski and Linder. Each of the
candidate models is studied under two different assumptions: as genuine
alternatives to $\Lambda$CDM (where a new degree of freedom would be expected
to explain the recent acceleration of the universe without any cosmological
constant) and as parametric extensions of $\Lambda$CDM (where both a
cosmological constant and the new mechanism can coexist, and the relative
contributions of both are determined by the data). Our comparative analysis
suggests that, from a phenomenological point of view, all such models neatly
divide into two classes, with different observational consequences.
