We have returned to the problem of the apparently diffuse gamma rays c
oming from extragalactic space, the energy range being 30 MeV-4 GeV. T
he return involves the use of somewhat more precise EGRET data (Phase
1 and 2 sky survey) than was used in our earlier work but more particu
larly a detailed analysis of the Inverse Compton contribution, of Gala
ctic origin. The ensuing extragalactic intensity is significantly lowe
r than hitherto and an interesting consequence is that the spectrum jo
ins rather nicely that estimated recently at lower energies using the
COMPTEL instrument. We have also made a rather speculative estimate of
the contribution from gamma rays produced in the Giant Galactic Halo
which has been claimed to extend to some 100 kpc from the sun. The con
clusion is that the truly extragalactic diffuse intensity could be muc
h lower than commonly estimated over a wide energy band. (C) 1997 Else
vier Science B.V.