For the case of a known data series a Monte Carlo technique is used to estimate how well a cubic spline method will reconstruct the original data when gaps are put in randomly, to allow the use of standard spectral analysis methods. A general result is that the adverse effects of the gaps increase most rapidly for the smallest percentages of data lost. The results depend very strongly on the amount of power in the frequency band of interest relative to the power at other frequencies. For a strong signal, rising well above the background, it was found that a loss of data of ~20% to 30%, if the length of the holes is only 1/3 to 1/2 the period of interest, will still allow an estimate of phase to ~10¿ at the 90% confidence level. The errors associated with loss of data are estimated as a function of strength of the signal, the size of the gaps, and the amount of data lost.