We have developed a generalised iterative scaling method (KRAS) that is able to balance and reconcile input-output tables and SAMs under conflicting external information and inconsistent constraints. Like earlier RAS variants, KRAS can: (a) handle constraints on arbitrarily sized and shaped subsets of matrix elements; (b) include reliability of the initial estimate and the external constraints; and (c) deal with negative values, and preserve the sign of matrix elements. Applying KRAS in four case studies, we find that, as with constrained optimisation, KRAS is able to find a compromise solution between inconsistent constraints. This feature does not exist in conventional RAS variants such as GRAS. KRAS can constitute a major advance for the practice of balancing input-output tables and Social Accounting Matrices, in that it removes the necessity of manually tracing inconsistencies in external information. This quality does not come at the expense of substantial programming and computational requirements (of conventional constrained optimisation techniques).