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The performance of collective operations has been a critical issue since the advent of MPI. Many algorithms have been proposed for each MPI collective operation but none of them proved optimal in all situations. Different algorithms demonstrate superior performance depending on the platform, the message size, the number of processes, etc. MPI implementations perform the selection of the collective algorithm empirically, executing a simple runtime decision function. While efficient, this approach does not guarantee the optimal selection. As a more accurate but equally efficient alternative, the use of analytical performance models of collective algorithms for the selection process was proposed and studied. Unfortunately, the previous attempts in this direction have not been successful. We revisit the analytical model-based approach and propose two innovations that significantly improve the selective accuracy of analytical models: (1) We derive analytical models from the code implementing the algorithms rather than from their high-level mathematical definitions. This results in more detailed models. (2) We estimate model parameters separately for each collective algorithm and include the execution of this algorithm in the corresponding communication experiment. We experimentally demonstrate the accuracy and efficiency of our approach using Open MPI broadcast and gather algorithms and a Grid5000 cluster.