The CCR model by Charnes, Cooper and Rhodes (1978) on the one hand and BCC model by Banker, Charnes and Cooper (1984) on the other hand are the most common used approaches of data envelopment analysis (DEA). If we measure efficiency of decision making units (DMUs) by the BCC model, technology is characterized by variable returns to scale. If the inputs and outputs of a DMU are scaled by two parameters such that the BCC (in)efficiency score is unchanged we call this adaptation a bicentric scaling (BS). We introduce a linear program to calculate the BS stability region of all DMUs, efficient or inefficient. Moreover we determine the scale efficiency within the stability region. The new approach is illustrated by a numerical example of European health services. We demonstrate the BS stability region for various states and illustrate consequences on scale efficiency. It is shown that some states can improve scale efficiency without losing BCC efficiency.