The authors study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number Re. They prove that for sufficiently regular initial data of size \(\epsilon \leq c_0\mathbf {Re}^-1\) for some universal \(c_0 > 0\), the solution is global, remains within \(O(c_0)\) of the Couette flow in \(L^2\), and returns to the Couette flow as \(t \rightarrow \infty \). For times \(t \gtrsim \mathbf {Re}^1/3\), the streamwise dependence is damped by a mixing-enhanced dissipation effect and the solution is rapidly attracted to the class of “2.5 dimensional” streamwise-independent solutions referred to as streaks.