  We report quasi-simultaneous GMRT observations of seven extragalactic radio
sources at 150, 325, 610 and 1400 MHz, in an attempt to accurately define their
radio continuum spectra, particularly at frequencies below the observed
spectral turnover. We had previously identified these sources as candidates for
a sharply inverted integrated radio spectrum whose slope is close to, or even
exceeds $\alpha_c$ = +2.5, the theoretical limit due to synchrotron
self-absorption (SSA) in a source of incoherent synchrotron radiation arising
from relativistic particles with the canonical (i.e., power-law) energy
distribution. We find that four out of the seven candidates have an inverted
radio spectrum with a slope close to or exceeding +2.0, while the critical
spectral slope $\alpha_c$ is exceeded in at least one case. These sources,
together with another one or two reported in very recent literature, may well
be the archetypes of an extremely rare class, from the standpoint of violation
of the SSA limit in compact extragalactic radio sources. However, the
alternative possibility that free-free absorption is responsible for their
ultra-sharp spectral turnover cannot yet be discounted.
