  We study the effect of variable jet bulk Lorentz factors, i.e., either jet
acceleration or deceleration, on partially synchrotron self-absorbed radio
spectra from cores of radio-loud active galactic nuclei and black-hole binaries
in the hard state. In about a half of quasars and radio galaxies, their core
radio spectra are observed to be soft, i.e., have the spectral index of
$\alpha<0$. If they are emitted by jets with constant Lorentz factors, that
softness implies deposition of large amounts of energy at large distances from
the centre. We show here that such soft spectra can be explained without that
energetic requirement by emission of jets with the Doppler factor increasing
with the distance. This can happen for either jet acceleration or deceleration,
depending on the jet viewing angle. We find our model can explain the quiescent
radio to X-ray spectra of the BL Lac objects Mrk 421 and Mrk 501.
