Submitted on 28 Jul 2007 (v1), last revised 30 Oct 2007 (this version, v5).-- 17 pages, 4 figures. References addedWe point out a generic inconsistency of the coupling of ordinary gravity as described by general relativity with matter invariant under the subgroup of unimodular diffeomorphisms (TDiffs), and some previously studied exceptions are pointed out. The most general Lagrangian invariant under TDiff up to dimension five operators is determined, and restrictions on parameters coming from existing observations are studied in some cases.This work has been partially supported by the European Commission (HPRN-CT-200-00148) and by FPA2003-04597 (DGI del MCyT, Spain), as well as Proyecto HEPHACOS (CAM); P-ESP-00346. A.F.F has been supported by a MEC grant, AP-2004-0921.Peer reviewed