  We obtain global well-posedness, scattering, uniform regularity, and global
$L^6_{t,x}$ spacetime bounds for energy-space solutions to the defocusing
energy-critical nonlinear Schr\"odinger equation in $\R\times\R^4$. Our
arguments closely follow those of Colliander-Keel-Staffilani-Takaoka-Tao,
though our derivation of the frequency-localized interaction Morawetz estimate
is somewhat simpler. As a consequence, our method yields a better bound on the
$L^6_{t,x}$-norm.
