9 pages, 6 figures.We discuss the cosmological degeneracy between the Hubble parameter H(z), the age of the universe and cosmological parameters describing simple variations from the minimal LCDM model. We show that independent determinations of the Hubble parameter H(z) such as those recently provided by Simon et al., Phys. Rev. D 71 (2005) 123001, combined with Cosmic Microwave Background data, can provide stringent constraints on possible deviations from the LCDM model. In particular we find that this data combination constrains at the 68% (95%) confidence level the following parameters: sum of the neutrino masses < 0.5 (1.0) eV, number of relativistic neutrino species N_rel = 4.1^{+0.4}_{-0.9} (^{+1.1}_{-1.5}), dark energy equation of state parameter w = -0.95 ± 0.17 (± 0.32), and curvature Ω_k = 0.002 ± 0.006 (± 0.014), in excellent agreement with dataset combinations involving Cosmic Microwave Background, Supernovae and Baryon Acoustic Oscillations.We acknowledge the use of the Legacy Archive for Microwave Background Data Analysis (LAMBDA). Support for LAMBDA is provided by the NASA Office of Space Science. DGF is supported by a FPU contract, with ref. AP2005-1092. LV acknowledges support of FP7-PEOPLE-2007-4-3-IRGn202182 and CSIC I3 grant 200750I034. RJ is supported by CSIC I3 grant and FP7-PEOPLE-2007-IRG. This work was supported in part by the Spanish Ministry of Education and Science (MEC) through the Consolider Ingenio-2010 program, under project CSD2007- 00060 Physics of the Accelerating Universe (PAU).Peer reviewed