Spectral simulation is used widely in electrical engineering to generate random fields with a given covariance spectrum. The algorithms used are fast particularly when based on Fast Fourier Transform (FFT). However, because of lack of phase identification, spectral simulation only generates unconditional realizations. Local data conditioning is obtained typically by adding a simulated kriging residual. This conditioning process requires an additional kriging at each simulated node thus forfeiting the speed advantage of FFT. A new algorithm for conditioning is proposed whereby the phase values are determined iteratively to ensure approximative data reproduction while reproducing the frequency spectrum, that is, the covariance model. A case study is presented to demonstrate the algorithm.