National Statistical Agencies (NSAs) have to guarantee that disseminated data do not provide individual confidential information. To achieve this goal, statistical disclosure control techniques have to be applied to real data before publication. In this work we consider a particular technique for tabular data named ``controlled tabular adjustment" (CTA). Given a statistical table, CTA looks for the closest safe table using some particular distance. In this work we focus on three-dimensional (3D) tables (i.e., tables obtained by crossing three variables) using the L1 distance. We show that L1-CTA in 3D tables can be formulated as a large linear optimization problem with block-angular structure. These problems are solved by a specialized interior-point algorithm for block-angular constraints matrices, which solves the normal equations by a combination of Cholesky factorization and preconditioned conjugate gradients. Computational results are reported for large instances, resulting in linear optimization problems of up to 50 millions variables and 25 millions constraints.