We develop methods for the variational design of algebraic curves. Our approach is based on truly geometric fairness criteria, such as the elastic bending energy. In addition, we take certain feasibility criteria for the algebraic curve segment into account. We describe a computational technique for the variational design of algebraic curves, using an SQP (sequential quadratic programming) – type method for constrained optimization. As demonstrated in this paper, the powerful techniques of variational design can be used not only for parametric representations, but also for curves in implicit form.