Generative Multimedia (GM) applications are an increasingly popular way to implement interactive media performances. Our contributions include creating a metric for evaluating Generative Multimedia performances, designing a model for accepting perceiver preferences, and using those preferences to adapt GM performances. The metric used is imprecision, which is the ratio of the actual computation time of a GM element to the computation time of a complete version of that GM element. By taking a perceiver's preferences into account when making adaptation decisions, applications can produce GM performances that meet soft real-time and resource constraints while allocating imprecision to the GM elements the perceiver least cares about. Compared to other approaches, perceiver-directed imprecision best allocates impreciseness while minimizing delay.