A globally controlled architecture for a quantum computer is highly appealing as one does not then require the technological capability of addressing each and every qubit within the device. Although several fully global controlled designs for a universal quantum computer have been proposed in the literature - and although it has been proven that a fully global fault tolerant (FT) quantum error correction scheme is possible in principle, no actual scheme for the latter has yet been advanced. In this work we go part way towards the latter and present a fault-tolerant semi-global control strategy for universal quantum computers. We show that an N-dimensional array of qubits where only (N − 1)-dimensional addressing resolution is available is compatible with FT universal quantum computation. What is more, we show that measurements and individual control of qubits are required only at the boundaries of the FT computer. Our model alleviates the heavy physical conditions on current qubit candidates imposed by addressability requirements and represents an option for improving their scalability.