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This paper proposes a pitch estimation algorithm that is based on optimal harmonic model fitting. The algorithm operates directly on the time-domain signal and has a relatively simple mathematical background. To increase its efficiency and accuracy, the algorithm is applied in combination with an autocorrelation-based initialization phase. For testing purposes we compare its performance on pitch-annotated corpora with several conventional time-domain pitch estimation algorithms, and also with a recently proposed one. The results show that even the autocorrelation-based first phase significantly outperforms the traditional methods, and also slightly the recently proposed yin algorithm. After applying the second phase - the harmonic approximation step - the amount of errors can be further reduced by about 20% relative to the error obtained in the first phase.