  We discuss the properties of the sources in the CLASS Blazar survey which
aims at the selection of low radio power (P(5GHz)<10^25 W Hz^-1) blazars. We
use VLA data from available catalogues and from our own observations to
constrain the radio core-dominance of the sample which, together with the flat
radio spectral index, is a signature of the blazar activity. X-ray data from
the ROSAT All Sky Survey were also collected in order to constrain the
radio-to-X-ray luminosity ratio (alpha_RX) of the sources. The data analysis
shows that more than 30% of sources at low radio power (P(5 GHz)<10^25 W Hz^-1)
have an alpha_RX steeper than that expected in the framework of the ``blazar
sequence'' recently put forward to unify the high and low power blazars. The
possibility that this result is influenced by contaminating sources in the
current sample is discussed. The conclusion is that, even if a number of
non-blazars (typically CSO/GPS sources) are expected in the survey, it is
unlikely that this constitutes the sole reason for the observed deviation. In
particular, we show 2 examples for which the blazar nature is confirmed from
VLBI data and for which the steep alpha_RX (suggesting a synchrotron peak
frequency below 10^15.5 Hz) and the low radio power (0.6-2x10^24 W Hz^-1) put
these sources outside the ``blazar sequence''. The results presented here show
the importance of a correct and unbiased sampling of the low-power regime of
the blazar population.
