  We show that the new type of "non-metric" gravity theories introduced
independently by Bengtsson and Krasnov can in fact be reexpressed explicitely
as a metrical theory coupled to an auxiliary field. We unravel why such
theories possess only one propagating graviton by looking at the quadratic
perturbation around a fixed solution. And we give a general construction
principle with a new class of example of such modified gravity theories still
possessing only two propagating degrees of freedom.
