This paper is concerned with the problem of deriving efficient operational rules for polling queues according to a fixed time polling scheme. A fixed time polling scheme specifies not only the visit order of the queues, but also the starting time for each visit. This problem arose from the need to efficiently collect files with call records from telecommunication switches. Using a simple approximation for the mean waiting times in a polling system with a non-cyclic visit order of the queues, we present an approach to the problem of minimizing a weighted sum of the mean waiting times at the various queues. This approach is tested via numerical experiments that are partly based on real network data.