Linear Context-Free Rewriting Systems (LCFRSs) are a grammar formalism capable of modeling discontinuous phrases. Many parsing applications use LCFRSs where the fan-out (a measure of the discontinuity of phrases) does not exceed 2. We present an efficient algorithm for optimal reduction of the length of production right-hand side in LCFRSs with fan-out at most 2. This results in asymptotical running time improvement for known parsing algorithms for this class.