  Recent data on CBR anisotropies show a Doppler peak higher than expected in
CDM cosmological models, if the spectral index $n=1$. However, CDM and LCDM
models with n>1 can hardly be consistent with LSS data. Mixed models, instead,
whose transfer function is naturally steeper because of free--streaming in the
hot component, may become consistent with data if n>1, when Omega_h is large.
This is confirmed by our detailed analysis, extended both to models with a hot
component whose momentum space distribution had a thermal origin (like massive
neutrinos), and to models with a non--cold component arising from heavier
particle decay. In this work we systematically search models which fulfill all
constraints which can be implemented at the linear level. We find that a
stringent linear constraint arises from fitting the extra-power parameter
Gamma. Other significant constraints arise comparing the expected abundances of
galaxy clusters and high-z systems with observational data. Keeping to models
with Gamma \geq 0.13, a suitable part of the space parameter still allows up to
\sim 30% of hot component (it is worth outlining that our stringent criteria
allow only models with 0.10 \mincir Omega_h \mincir 0.16, if n \leq 1). We also
outline that models with such large non--cold component would ease the solution
of the so--called baryon catastrophe in galaxy clusters.
