We consider the design of the linear precoder for a multiple-input single-output (MISO) downlink in a system that employs limited feedback using Grassmannian quantization. The goal is to minimize the outage probability of a target signal-to-interference-andnoise ratio (SINR) under a transmitted power constraint. By approximating the outage constraint by a zero-outage region, employing a semidefinite relaxation, and applying an extension of the S-Lemma, the problem is converted into a quasi-convex problem. Insights into the structure of the solution of that problem generate an alternate design formulation that provides greater robustness in the presence of significant uncertainties and has a quasi-closed form solution.