  In a previous paper we showed that the radio sources selected by combining
large areas radio and optical surveys, present a strong deficit of radio
emission with respect to 3CR radio-galaxies matched in line emission
luminosity. We argued that the prevalence of sources with luminous extended
radio structures in high flux limited samples is due to a selection bias.
Sources with low radio power form the bulk of the radio-loud AGN population but
are still virtually unexplored.
  We here analyze their photometric and spectroscopic properties. From the
point of view of their emission lines, the majority of the sample are Low
Excitation Galaxies (LEG), similar to the 3CR objects at the same level of line
luminosity. The hosts of LEG are red, massive Early-Type Galaxies (ETG) with
large black holes masses , statistically indistinguishable from the hosts of
low redshift 3CR/LEG sources. No genuine radio-loud LEG could be found
associated with black holes with a mass substantially lower than 10^8 M(sun) or
with a late type host. The fraction of galaxies with signs of star formation
(5%) is similar to what is found in both the quiescent ETG and 3CR/LEG hosts.
We conclude that the deficit in radio emission cannot be ascribed to
differences in the properties of their hosts. We argue that instead this could
be due to a temporal evolution of the radio luminosity.
  A minority (10%) of the sample show rather different properties, being
associated with low black hole masses, with spiral galaxies, or showing a high
excitation spectrum. In general these outliers are the result of the
contamination from Seyfert and from galaxies where the radio emission is
powered by star formation. For the objects with high excitation spectra there
is no a clear discontinuity in either the host or nuclear properties as they
span from radio-quiet and radio-loud AGN.
