Improvements in text generation technologies such as machine translation have necessitated more costly and time-consuming human evaluation procedures to ensure an accurate signal. We investigate a simple way to reduce cost by reducing the number of text segments that must be annotated in order to accurately predict a score for a complete test set. Using a sampling approach, we demonstrate that information from document membership and automatic metrics can help improve estimates compared to a pure random sampling baseline. We achieve gains of up to 20% in average absolute error by leveraging stratified sampling and control variates. Our techniques can improve estimates made from a fixed annotation budget, are easy to implement, and can be applied to any problem with structure similar to the one we study.