We address the problem of filtering out localized time-frequency components in signals. The problem is formulatedas a minimization of a suitable quadratic form, that involves adata fidelity term on the short-time Fourier transform outsidethe support of the undesired component, and an energy pe-nalization term inside the support. The minimization yields alinear system whose solution can be expressed in closed formusing Gabor multipliers. We provide an analysis of the solu-tion and its approximation by truncated eigenvalue expansion,and illustrate its performance on synthetic mixtures of audiosignals. The proposed approach outperforms approaches thatare routinely used in applications.