The Computational Grid provides a promising platform for the efficient execution of parameter sweep applications over very large parameter spaces. Scheduling such applications is challenging because target resources are heterogeneous, because their load and availability varies dynamically, and because independent tasks may share common data files.In this paper, we propose an adaptive scheduling algorithm for parameter sweep applications on the Grid. We modify standard heuristics for task/host assignment in perfectly predictable environments (Max-min, Min-min, Sufferage), and we propose an extension of Sufferage called XSufferage. Using simulation, we demonstrate that XSufferage can take advantage of file sharing to achieve better performance than the other heuristics.We also study the impact of inaccurate performance prediction on scheduling. Our study shows that: (i)~different heuristics behave differently when predictions are inaccurate; (ii)~increased adaptivity leads to better performance.