  We allow a more general (step-function) form of the primordial power spectrum
than the usual featureless power-law Harrison--Zeldovich (with spectral index
n=1) power spectrum, and fit it to the latest Cosmic Microwave Background data
sets. Although the best-fitting initial power spectrum can differ significantly
from the power-law shape, and contains a bump at scales k ~ 0.003 h/Mpc, we
find Omega_m to be approximately 0.24, consistent with previous analyses that
assume power-law initial fluctuations. We also explore the feasibility of the
2dF and SDSS galaxy redshifts surveys to observe these features, and we find
that even if features exist in the primoridal power spectrum, they are washed
out by the window functions of the redshift surveys on scales k< 0.03 h/Mpc.
