El Niño Southern Oscillation (ENSO) is the leading mode of interannual climate variability, with large socioeconomical and environmental impacts. The main conceptual model for ENSO, the Recharge Oscillator (RO), considers two independent modes: the fast zonal tilt mode in phase with central-eastern Pacific Temperature (Te), and the slow recharge mode in phase quadrature. However, usual indices (western or equatorial sea level/thermocline depth h) do not orthogonally isolate the slow recharge mode, leaving it correlated with Te. Furthermore the optimal index is currently debated. Here, we develop an improved recharge index by objectively optimizing the RO equations fit to observations. (a) Te-variability is regressed out, to build hind statistically-independent from Te. Capturing the pure recharge, hind reconciles usual indices. (b) The optimum is equatorial plus southwestern Pacific hind_eq+sw (because of ENSO Ekman pumping meridional asymmetry). Using hind_eq+sw, the RO becomes more consistent with observations. hind_eq+sw is more relevant for ENSO operational diagnostics.