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When Cold Dark Matter (CDM) power spectrum normalized by COBE results, itsamplitude at smaller scales can be parametrized by $\Gamma\sim\Omega_0h$. Theexpected variations of Hubble flows in two samples, the sample of 36 clustersin the Mark III catalogue, and the sample of 20 Type Ia supernovae (SNe), arecalculated for the power spectrum in critical-density CDM models (includingtilted CDM models and vacuum-dominated CDM models). The comparison between theexpectations and the real variations in the data offers a bias-free way toconstrain the power spectrum. The cluster sample yields $\Gamma\le0.30-0.88(n_{ps}-1)+1.9 (n_{ps}-1)^2$ at 95% C.L., with best fits $\Gamma =0.15-0.39(n_{ps}-1)+0.37(n_{ps}-1)^2$, where $n_{ps}$ is the spectral index ofthe power spectrum. The Type Ia SN sample yields $\Gamma\le0.25-0.80(n_{ps}-1)+1.6 (n_{ps}-1)^2$ at 95% C.L., strongly favoring lower$\Gamma$'s. The results are inconsistent with a critical-densitymatter-dominated universe with $n_{ps}\ga 0.8$ and $H_0\ga 50$ km/sec/Mpc.Comment: 3 latex pages, 2 figures. Revised versio

Measuring the cold dark matter power spectrum from variations of Hubble flows