  We present two new covariant and general prescriptions for averaging scalar
observables on spatial regions typical of the observed sources and intersecting
the past light-cone of a given observer. One of these prescriptions is adapted
to sources exactly located on a given space-like hypersurface, the other
applies instead to situations where the physical location of the sources is
characterized by the experimental "spread" of a given observational variable.
The geometrical and physical differences between the two procedures are
illustrated by computing the averaged energy flux received by distant sources
located on (or between) constant redshift surfaces, and by working in the
context of a perturbed $\Lambda$CDM geometry. We find significant numerical
differences (of about ten percent or more, in a large range of redshift) even
limiting our model to scalar metric perturbations, and stopping our
computations to the leading non-trivial perturbative order.
