In this paper, the problem of estimating the frequencies, dampings, amplitudes and phases of closely spaced complex damped exponentials in the presence of noise is considered. In several papers, decimation is proposed as a way to increase the performance of subspace-based parameter estimation methods, in the case of oversampling (Signal Process. 63(3) (1997) 211; IEEE Signal Process. Lett. 4(2) (1997) 49; in: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Vol, V, Salt Lake City, UT, USA, May 7-11, 2001, pp. 3073-3076). In this paper, three decimative versions of the HTLS-method (J. Magn. Resonance A 110(2) (1994) 228), a subspace-based parameter estimation technique that operates directly on the data matrix, are derived and compared. Monte-Carlo simulation experiments show the influence of decimation on the statistical accuracy and the computational complexity of the algorithms. (C) 2003 Elsevier Science B.V. All rights reserved.