We illustrate how recently improved low-redshift cosmological measurements can tighten constraints on neutrino properties. In particular we examine the impact of the assumed cosmological model on the constraints. We first consider the new HST H0 = 74.2±3.6 measurement by Riess et al. (2009) and the σ8(Ωm/0.25)0.41 = 0.832±0.033 constraint from Rozo et al. (2009) derived from the SDSS maxBCG Cluster Catalog. In a ΛCDM model and when combined with WMAP5 constraints, these low-redshift measurements constrain ∑mν < 0.4 eV at the 95% confidence level. This bound does not relax when allowing for the running of the spectral index or for primordial tensor perturbations. When adding also Supernovae and BAO constraints, we obtain a 95% upper limit of ∑mν < 0.3eV. We test the sensitivity of the neutrino mass constraint to the assumed expansion history by both allowing a dark energy equation of state parameter w≠−1 and by studying a model with coupling between dark energy and dark matter, which allows for variation in w, Ωk, and dark coupling strength ξ. When combining CMB, H0 and the SDSS LRG halo power spectrum from Reid et al. 2009, we find that in this very general model, ∑mν < 0.51 eV with 95% confidence. If we allow the number of relativistic species Nrel to vary in a ΛCDM model with ∑mν = 0, we find Nrel = 3.76+0.63−0.68(+1.38−1.21) for the 68% and 95% confidence intervals. We also report prior-independent constraints, which are in excellent agreement with the Bayesian constraints.