A physical understanding of the behaviour of cold ultra-dense matter -- at and above nuclear density -- can only be achieved by the study of neutron stars. The recent 1.97+/-0.04 Msun measurement for PSR 1614-2230 suggests that strange quark matter and hyperons/kaons condensate EoSs are disfavoured, in favour of hadronic "normal matter" EoSs. Over much of the neutron star mass-radius parameter space, the latter EoSs produce lines of quasi-constant radii (within the measurement uncertainties, of about 10%). We present a simultaneous spectral analysis of several globular cluster quiescent low-mass X-ray binaries where we require the radius to be the same among all neutron stars analyzed. Our results suggest a neutron star radius much smaller than previously reported, with a value Rns = 9.1 (+1.3)(-1.5) km, at 90% confidence, using conservative assumptions. The Markov-Chain Monte-Carlo method and the Bayesian approach developed in this analysis permits including uncertainties in the distance, in the hydrogen column density, and possible contributions to the spectra due to unmodelled spectrally hard components.