Dealing with time series with missing values, including those afflicted by low quality or over-saturation, presents a significant signal processing challenge. The task of recovering these missing values, known as imputation, has led to the development of several algorithms. However, we have observed that the efficacy of these algorithms tends to diminish when the time series exhibit non-stationary oscillatory behavior. In this paper, we introduce a novel algorithm, coined Harmonic Level Interpolation (HaLI), which enhances the performance of existing imputation algorithms for oscillatory time series. After running any chosen imputation algorithm, HaLI leverages the harmonic decomposition based on the adaptive nonharmonic model of the initial imputation to improve the imputation accuracy for oscillatory time series. Experimental assessments conducted on synthetic and real signals consistently highlight that HaLI enhances the performance of existing imputation algorithms. The algorithm is made publicly available as a readily employable Matlab code for other researchers to use.