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Several algorithms for the spectral analysis of irregularly sampled random processes can estimate the spectral density for a low frequency range. A new time-series method extended that frequency range with a factor of thousand or more. The new algorithm has two requirements to give useful results. First, at least ten closest pairs of neighboring irregular observations should have a distance less than the minimum resampling distance for the chosen discrete-time frequency range. Second, a low-order time-series model should be appropriate to describe the global character of the data. The consequences and importance of this second demand are studied for irregular turbulence observations with narrow spectral details. Models of low orders are estimated from equidistant hot-wire observations and from irregularly sampled laser Doppler anemometer (LDA) data, which are obtained from the same turbulence process. The irregular data are resampled with the nearest neighbor method, both with and without slotting. Apart from the usual bias contributions of resampling irregular data, LDA data can give an additional spectral bias if the instantaneous sampling rate is correlated to the actual magnitude of the turbulent velocity. Making histograms of the amplitudes and the interarrival times provides useful information about irregularly sampled data.