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 .