This paper addresses the problem of phase cycle-slip (FM click noise) elimination. For analyses and application demonstration, the signal of interest is a commercial FM transmission, received and sampled for subsequent demodulation as typical in software defined radios. There are two parts to this paper. The first part will investigate the advantages of using data fitting to repair the time series in the neighbourhood of a detected click. Previous papers (e.g., [1]) have considered time series which have neighbourhoods in which only one point was considered as a click, and hence, only one point needed to be repaired. We will consider the more difficult and practical case where there is a frequency modulated signal passed through a band-pass filter and a (software/digital) FM limiter discriminator used for demodulation. This receive system has the effect of causing click distortion over multiple samples, making the repairing that much more difficult. The methods of forward-backward linear prediction (FBLP or Wiener filtering), least squares polynomial fitting (LSPOLY), and twin Tukey window (TTW) filtering are discussed. The results are shown empirically, and will show that the TTW technique outperforms the FBLP and LSPOLY techniques for the presented application. The second part of this paper will discuss potential techniques to discern samples which are clicks, from samples which are normal yet click-like. We will consider the combination of autocorrelation, kurtosis, 4th order moment, and spectral characteristics, to form a threshold detection level to identify clicks.