  Recent neutrino oscillation data hint that the smallest neutrino mixing angle
theta_{13} is possible to lie in the range 5^\circ \lesssim \theta_{13}
\lesssim 12^\circ. We show that reasonable perturbations to the democratic
mixing pattern, which is geometrically related to the tri-bimaximal mixing
pattern through an equal shift \theta_* \simeq 9.7^\circ of two large mixing
angles, can naturally produce a nearly tri-bimaximal neutrino mixing matrix V
with sufficiently large theta_{13}. Two especially simple but viable scenarios
of V are proposed and their phenomenological consequences are discussed.
