Energy liberation rate (E) during steady muscle shortening is a monotonic increasing or biphasic function of the shortening velocity (V). The study examines three plausible hypotheses for explaining the biphasic E-V relationship (EVR): 1) the cross-bridge (XB) turnover rate from non-force-generating (weak) to force-generating (strong) conformation decreases as V increases; 2) XB kinetics is determined by the number of strong XBs (XB-XB cooperativity); and 3) the affinity of troponin for calcium is modulated by the number of strong XBs (XB-Ca cooperativity). The relative role of the various energy-regulating mechanisms is not well defined. The hypotheses were tested by coupling calcium kinetics with XB cycling. All three hypotheses yield identical steady-state characteristics: 1) hyperbolic force-velocity relationship; 2) quasi-linear stiffness-force relationship; and 3) biphasic EVR, where E declines at high V due to decrease in the number of cycling XBs or in the weak-to-strong transition rate. The hypotheses differ in the ability to describe the existence of both monotonic and biphasic EVRs and in the effect of intracellular free calcium concentration ([Ca2+]i) on the EVR peak. Monotonic and biphasic EVRs with a shift in EVR peak to higher velocity at higher [Ca2+]i are obtained only by XB-Ca cooperativity. XB-XB cooperativity provides only biphasic EVRs. A direct effect of V on XB kinetics predicts that EVR peak is obtained at the same velocity independently of [Ca2+]i. The study predicts that measuring the dependence of the EVR on [Ca2+]i allows us to test the hypotheses and to identify the dominant energy-regulating mechanism. The established XB-XB and XB-Ca mechanisms provide alternative explanations to the various reported EVRs.