In an economical system with only two heavy right-handed neutrinos, we postulate a new texture for 3 x 2 Dirac mass matrix m(D). This model implies one massless light neutrino and thus displays only two patterns of mass spectrum for light neutrinos, namely hierarchical or inverse-hierarchical. Both the cases can correctly reproduce all the current neutrino oscillation data with a unique prediction m(nu e nu e) = root Delta m(solar)(2)/3 and root Delta(2)(atm) for the hierarchical and the inverse-hierarchical cases, respectively, which can be tested in next generation neutrino-less double beta decay experiments. Introducing a single physical CP phase in in m(D), we examine baryon asymmetry through leptogenesis. Interestingly, through the CP phase there are correlations between the amount of baryon asymmetry and neutrino oscillation parameters. We find that for a fixed CP phase, the hierarchical case also succeeds in generating the observed baryon asymmetry in our universe, plus a non-vanishing U-e3 which is accessible in future baseline neutrino oscillation experiments. (c) 2008 Published by Elsevier B.V.