Nematic elastomers are rubbery solids which have liquid crystals incorporated into their polymer chains. These materials display many unusual mechanical properties, one such being the ability to form fine-scale microstructure. In this work, we explore the response of taut and appreciably stressed sheets made of nematic elastomer. Such sheets feature two potential instabilities – the formation of fine-scale material microstructure and the formation of fine-scale wrinkles. We develop a theoretical framework to study these sheets that accounts for both instabilities, and we implement this framework numerically. Specifically, we show that these instabilities occur for distinct mesoscale stretches, and observe that microstructure is finer than wrinkles for physically relevant parameters. Therefore, we relax (i.e., implicitly but rigorously account for) the microstructure while we regularize (i.e., compute the details explicitly) the wrinkles. Using both analytical and numerical studies, we show that nematic elastomer sheets can suppress wrinkling by modifying the expected state of stress through the formation of microstructure.