Choking under pressure (CUP) research shows that individuals working on higher-order cognitive tasks do not benefit from higher working memory (WM) capacity under pressure. This CUP effect, or reduced WM/performance link, entails that high working memory individuals (high WMs) perform at about the same level as low WMs. However, it still is an open question which specific components create a high pressure situation. We hypothesized that CUP effects should occur in situations where high WMs are faced with a self-improvement goal, particularly when they do not have much room to improve their performance any further. Study 1 demonstrated that the positive WM/math performance link was reduced in the mere presence of a self-improvement goal. Study 2 further showed that the WM/math performance link was only reduced when self-improvement instructions emphasized that there was not much room left for improvement. Discussion focuses on implications for both CUP and achievement goal research.