Two new methods (Maximum Likelihood Method or MLM, and Maximum Entropy Method or MEM) for power spectral density estimation have been experimentally investigated. Both methods, unlike conventional methods, adapt to the actual characteristics of the noise process under study. The new techniques are particularly valuable if the process contains one or more narrow peaks in frequency which are to be resolved. In this case, the output peaks from MEM are proportional to the square of the power in the narrow peaks but the area is equal to power. The peak values of the MLM reflect power directly. Both methods yield the true spectrum if the spectrum changes slowly enough with frequency. Neither of the new methods appears to be unduly sensitive to small statistical fluctuations of the estimated correlation function used to obtain spectral estimates.