Most speech enhancement algorithms focus on obtaining an estimator relying on stochastic models. In this paper, a minimum mean-square error (MMSE) estimator under a stochastic– deterministic model is proposed where a heavy-tail distribution called t-Location-Scale (tls) is used for modeling Discrete Fourier Transform coefficients of clean speech signals and exponential and sinusoidal models are employed as deterministic models. In the exponential model, the frequency and damping coefficient are estimated by using the Matrix Pencil method. Also, in previous studies, the number of exponential components in the deterministic model for stochastic-deterministic speech enhancement algorithm has been considered to be one. In this paper, the corresponding exponential model is developed to have an arbitrary number of exponential components. The speech enhancement experiments are performed in three modes, exponential-Gaussian (the first proposed method), exponential-tls (the second proposed method), and sinusoidal-Gaussian. Comparisons are made with the exponential-Gaussian method (with only one exponential component), as well as with the Weiner and tls stochastic estimators. The implementation results in the presence of six noise types from Noisex-92 dataset show that the two proposed methods improve the segSNR values and have quite similar PESQ values comparing with the stochastic based speech enhancement methods.