  CDM models with non-scale-free step-like spectra of adiabatic perturbations
produced in a realistic double inflationary model are compared with recent
observational data. The model contains two additional free parameters
relatively to the standard CDM model with the flat ($n=1$) initial spectrum.
Results of the COBE experiment are used for the determination of a free overall
spectrum normalization. Then predictions for the galaxy biasing parameter, the
variance for "counts in cells", the galaxy angular correlation function, bulk
flow peculiar velocities and the Mach number test are obtained. Also considered
are conditions for galaxy and quasar formation. Observational data strongly
restricts allowed values for the two remaining model parameters. However, a
non-empty region for them satisfying all considered tests is found.
