Games can invite players to try on moral identities, but players ultimately choose how to respond to this invitation. In this study, I explore how the design of a game and the context it is played in affect whether players tried on a moral identity when completing in-game actions. I interviewed seven students who had played an ethics game and asked what influenced their perception of the game's ethical significance. After coding interview transcripts using an established framework of design and contextual features related to serious games, I found that environmental constraints, formal constraints, goals, and the game context all influenced whether students tried on moral identities during the game, suggesting a complicated relationship between player identity, game design, and game context.