Spectral analyses of the Greenland Ice Sheet Project 2 (GISP2) δ18O record has been interpreted to show a 1/(1470 yr) spectral peak that is highly statistically significant (p<0.01) relative to a null model, H0, consisting of an auto-regressive order one process. In this study H0 is generalized using an auto-regressive moving-average process that is removed from the GISP2 δ18O time series, yielding a spectral estimate that is approximately level. A rule of thumb is proposed for evaluating the adequacy of H0 involving comparing the expected and observed variance of the logarithm of a leveled spectral estimate. After suitably leveling GISP2 δ18O and accounting for multiple hypothesis testing, multitaper spectral estimation indicates that the 1/(1470 yr) peak is insignificant (p>0.05). The proposed techniques for fitting H0 should be generally applicable to evaluating peaks in other geophysical spectral estimates.