Inspired by surface mesh simplification methods, we present a technique for reducing the number of Bézier curves in a vector graphics while maintaining high fidelity. We propose a curve-to-curve distance metric to repeatedly conduct local segment removal operations. By construction, we identify all possible lossless removal operations ensuring the smallest possible zero-error representation of a given design. Subsequent lossy operations are computed via local Gauss-Newton optimization and processed in a priority queue. We tested our method on the OpenClipArts dataset of 20,000 real-world vector graphics images and show significant improvements over representative previous methods. The generality of our method allows us to show results for curves with varying thickness and for vector graphics animations.