The compiler optimizations we enable and the order in which we apply them on a program have a substantial impact on the program execution time. Compilers provide default optimization sequences which can give good program speedup. As the default sequences have to optimize programs with different characteristics, they embed in them multiple subsequences which can optimize different classes of programs. These multiple subsequences may falsely interact with each other and affect the potential program speedup achievable. Instead of searching for a single universally optimal sequence, we can construct a small set of good sequences such that for every program class there exists a near-optimal optimization sequence in the good sequences set. If we can construct such a good sequences set which covers all the program classes in the program space, then we can choose the best sequence for a program by trying all the sequences in the good sequences set. This approach completely circumvents the need to solve the program classification problem. Using a sequence set size of around 10 we got an average speedup up to 14% on PolyBench programs and up to 12% on MiBench programs. Our approach is quite different from either the iterative compilation or machine-learning-based prediction modeling techniques proposed in the literature so far. We use different training and test datasets for cross-validation as against the Leave-One-Out cross-validation technique.