We propose a method for blindly separating real environment speech signals with as little distortion as possible in the special case where speech signals outnumber sensors. Our idea consists in combining sparseness with the use of an estimated mixing matrix. First, we use a geometrical approach to perform a preliminary separation and to detect when only one source is active. This information is then used to estimate the mixing matrix. Then we remove one source from the observations and separate the residual signals with the inverse of the estimated mixing matrix. Experimental results in a real environment (T/sub R/=130 ms and 200 ms) show that our proposed method, which we call sparseness-mixing matrix estimation (SMME), provides separated signals of better quality than those extracted by using only the sparseness property of the speech signal.