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The provision of Quality of Service (QoS) in Grids (systems made of heterogeneous computing resources geographically dispersed) is still a challenging task that needs the attention of the research community. Since reservations of resources may not always be possible, another possible way of enhancing the QoS perceived by Grid users is by performing meta-scheduling of jobs in advance, where jobs are scheduled some time before they are actually executed. Hence, it becomes more likely that the appropriate resources are available to run the job whenever needed. One of the drawbacks of this scenario is that fragmentation appears as a well known effect in job allocations into resources. Fragmentation also becomes the cause for poor resource utilization. For these reasons, a new technique has been developed to tackle fragmentation problems, which consists of rescheduling already scheduled tasks. To this end, some heuristics have been implemented to figure out which intervals need replanning and to select the jobs which are involved in that rescheduling process. On top of that, another heuristic has been implemented to put rescheduled jobs as close together as possible so that fragmentation is avoided or reduced to the minimum. This technique has been tested using a real test bed involving heterogeneous computing resources from different organizations. An evaluation is presented that illustrates the efficiency of this approach to meet the users' QoS requirements.