This paper introduces a new control topology for converter-interfaced wind turbines. Through a singular perturbation decomposition of the system dynamics, a controller is designed that isolates wind-power fluctuations from the power grid. Specifically, the controller causes the closed-loop wind turbine to behave as a simple first-order power filter, where power injected into the grid is a low-pass filtered version of the incident wind power. It is shown that a turbine hub-speed instability imposes a limit on the largest filtering time constant that may be safely implemented. A linearized analysis is used to calculate how a small filter time constant can be implemented to obtain regulation of the tip-speed ratio for the widest range of frequencies. The methodology thus offers the possibility to either deliver a filtered power at suboptimal conversion efficiency or track peak wind power. It is mathematically demonstrated that the control structure achieves the regulation of torsional dynamics and the dc-link capacitor voltage without involving the grid-side converter controls, thus eliminating the influence of those dynamics on the grid. Simulation studies are used to demonstrate the methodology's viability and explore the associated tradeoffs.