Let \(X\) be a Stein manifold of complex dimension \(n\) at least 2. This paper proves the following theorem on solving \(\bar\partial\) with a support condition. Theorem 1. Let \(\Omega\subset X\) be a relatively compact weakly \(q\)-pseudoconvex domain with \(C^2\) boundary. For any \(q\leq s\leq n\) and for \(f\in L_{r,s}^2(\Omega)\), \(\operatorname{supp} f\subset \bar\Omega\), satisfying \(\bar\partial f=0\) in the distribution sense in \(X\), there exists \(u\in L_{r,s-1}^2(\Omega)\), \(\operatorname{supp} u\subset\bar\Omega\) such that \(\bar\partial u=f\) in the distribution sense in \(X\). The proof uses classical \(L^2\)-methods and follows section 9.1 in the book by \textit{S.-C. Chen} and \textit{M.-C. Shaw} [Partial differential equations in several complex variables. Providence, RI: American Mathematical Society (2001; Zbl 0963.32001)].