This paper proposes a new approach to the regionalization of national input-output tables where suitable regional data are scarce and analysts are considering using location quotients (LQs). We focus on the FLQ formula, which frequently yields the best results of the pure LQ-based methods, and develop an enhanced way of implementing this approach. We use a modified cross-entropy (MCE) method, along with a regression model, to estimate values of the unknown parameter δ in the FLQ formula, specific to both region and country. An analysis of survey-based data for 16 South Korean regions reveals that the proposed FLQ+ approach yields more accurate estimates of both input coefficients and sectoral output multipliers than those from simpler LQ-based methods or the MCE approach alone. Sectoral outputs (or employment) are the only regional data required. The MCE method also clearly outperforms GRAS.