  We give sufficient conditions for compactness of localization operators on
modulation spaces $\textbf{M}^{p,q}_{m_{\lambda}}( \mathbb{R}^{d})$ of
$\omega$-tempered distributions whose short-time Fourier transform is in the
weighted mixed space $L^{p,q}_{m_\lambda}$ for
$m_\lambda(x)=e^{\lambda\omega(x)}$.
