  We prove global well-posedness for the cubic, defocusing, nonlinear
Schr{\"o}dinger equation on $\mathbf{R}^{2}$ with data $u_{0} \in
H^{s}(\mathbf{R}^{2})$, $s > 1/4$. We accomplish this by improving the almost
Morawetz estimates in [9].
