Various works have suggested that the Bondi--Sachs--Penrose decay conditions
on the gravitational field at null infinity are not generally representative of
asymptotically flat space--times. We have made a detailed analysis of the
constraint equations for ``asymptotically hyperboloidal'' initial data and find
that log terms arise generically in asymptotic expansions. These terms are
absent in the corresponding Bondi--Sachs--Penrose expansions, and can be
related to explicit geometric quantities. We have nevertheless shown that there
exists a large class of ``non--generic'' solutions of the constraint equations,
the evolution of which leads to space--times satisfying the
Bondi--Sachs--Penrose smoothness conditions.Comment: 8 pages, revtex styl