Covered call strategies are formed by selling a call option while holding the option's underlying asset. They are popular in asset management and are prominently featured in a number of institutional funds. Existing literature has typically comprised of descriptive analysis of the performance of covered calls when varying moneyness and maturity of the shorted call options, and using different underlying holdings. We propose using optimization to construct risk-return efficient covered call strategies. We first built a model to construct optimal covered call strategies on a single underlying asset, then generalized the model to simultaneously select equity positions and short call positions to form a portfolio of covered calls. The optimal covered calls exhibit a structured policy which provides insight into the nature of their performance.