  We obtain a complete description of closed ideals of the algebra
$\mathcal{D}\cap \mathrm{lip}_\alpha},$ $0<\alpha\leq{1/2},$ where
$\mathcal{D}$ is the Dirichlet space and $\mathrm{lip}_\alpha}$ is the algebra
of analytic functions satisfying the Lipschitz condition of order $\alpha.$
