  Infrared-Faint Radio Sources (IFRS) represent an unexpected class of objects
relatively bright at radio wavelength, but unusually faint at infrared (IR) and
optical wavelengths. A recent and extensive campaign on the radio-brightest
IFRSs (S_{1.4GHz} >= 10 mJy) has provided evidence that most of them (if not
all) contain an AGN. Still uncertain is the nature of the radio-faintest ones
(S_{1.4GHz} <= 1 mJy). The scope of this paper is to assess the nature of the
radio-faintest IFRSs, testing their classification and improving the knowledge
of their IR properties making use of the most sensitive IR survey available so
far: the Spitzer Extragalactic Representative Volume Survey (SERVS). We also
explore how the criteria of IFRSs can be fine-tuned to pinpoint radio-loud AGNs
at very high redshift (z > 4). We analysed a number of IFRS samples identified
in SERVS fields, including a new sample (21 sources) extracted from the Lockman
Hole. 3.6 and 4.5 mum IR counterparts of the 64 sources located in the SERVS
fields were searched for, and, when detected, their IR properties were studied.
We compared the radio/IR properties of the IR-detected IFRSs with those
expected for a number of known classes of objects. We found that they are
mostly consistent with a mixture of high-redshift (z >= 3) radio-loud AGNs. The
faintest ones (S_{1.4GHz} ~ 100 muJy), however, could be also associated with
nearer (z ~ 2) dust-enshrouded star-burst galaxies. We also argue that, while
IFRSs with radio-to-IR ratios > 500 can very efficiently pinpoint radio-loud
AGNs at redshift 2 < z < 4, lower radio-to-IR ratios (~ 100--200) are expected
for higher redshift radio-loud AGNs.
