A computationally efficient fast maximum-likelihood (FML) estimation scheme, which makes use of the shape of the surface of the compressed likelihood function (CLF), is proposed. The scheme uses only multiple one-dimensional searches oriented along appropriate ridges on the surface of the CLF. Simulations indicate that the performances of the proposed estimators match those of the corresponding maximum-likelihood estimators with very high probability. The approach is demonstrated by applying it to two different problems. The first problem involves the estimation of time of arrival and Doppler compression of a wideband hyperbolic frequency modulated (HFM) active sonar signal buried in reverberation. The second problem deals with estimating the frequencies of sinusoids. A threshold analysis of the proposed scheme is carried out to predict the signal-to-noise ratio (SNR) at which large estimation errors begin to occur, i.e., the threshold SNR, and its computational complexity is discussed.