We use microlocal and paradifferential techniques to obtain$L$^{8}norm bounds for spectral clusters associated with elliptic second-order operators on two-dimensional manifolds with boundary. The result leads to optimal$L$^{$q$}bounds, in the range 2⩽q⩽∞, for$L$^{2}- normalized spectral clusters on bounded domains in the plane and, more generally, for two-dimensional compact manifolds with boundary. We also establish new sharp$L$^{$q$}estimates in higher dimensions for a range of exponents q̅_{n}⩽$q$⩽∞.