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We present a method for stabilizing handheld video that simulates the camera motions cinematographers achieve with equipment like tripods, dollies, and Steadicams. We formulate a constrained convex optimization problem minimizing the $\ell_1$-norm of the first three derivatives of the stabilized motion. Our approach extends the work of Grundmann et al. [9] by solving with full homographies (rather than affinities) in order to correct perspective, preserving linearity by working in log-homography space. We also construct crop constraints that preserve field-of-view; model the problem as a quadratic (rather than linear) program to allow for an $\ell_2$ term encouraging fidelity to the original trajectory; and add constraints and objectives to reduce distortion. Furthermore, we propose new methods for handling salient objects via both inclusion constraints and centering objectives. Finally, we describe a windowing strategy to approximate the solution in linear time and bounded memory. Our method is computationally efficient, running at 300fps on an iPhone XS, and yields high-quality results, as we demonstrate with a collection of stabilized videos, quantitative and qualitative comparisons to [9] and other methods, and an ablation study.