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, by objectively optimizing the RO equations fit to observations, we develop an improved recharge index. (1) Te-variability is regressed out, building h_ind statistically-independent from Te. Capturing the pure recharge, h_ind reconciles usual indices. (2) The optimum is equatorial plus southwestern Pacific h_ind_eq+sw (because of ENSO Ekman pumping meridional asymmetry). Using h_ind_eq+sw, the RO becomes more consistent with observations. h_ind_eq+sw is more relevant for ENSO operational diagnostics.