Summary: Let \({\mathcal A}\) be a unital maximal full algebra of operator fields with base space \([0,1]^k\) and fibre algebras \(\{{\mathcal A}_t\}^k_{t\in[0,1]}\). It is shown in this paper that the stable rank of \({\mathcal A}\) is bounded above by the quantity \(\sup_{t\in[0,1]^k}\text{sr}(C([0,1]^k)\otimes{\mathcal A}_t)\), where `sr' means stable rank. Using the above estimate, the stable ranks of the \(C^*\)-algebras of the (possibly higher rank) discrete Heisenberg groups are computed.