This paper shows some new results concerning the influence of operating conditions on the phenomenon known as “coup de fouet”, a voltage drop which occurs at the beginning of the discharge of lead-acid batteries (LABs) previously fully charged. Even if this phenomenon is often suggested for diagnosing the state-of-charge (SOC) and the state-of-health (SOH) of LABs, it remains badly understood. Furthermore, this study deals with other transient voltage responses of LABs to galvanostatic polarisations that depend on their SOC, either on discharge or on charge. A special attention is paid to a phenomenon occurring at the beginning of the charge of these batteries after a full discharge, and which can be compared to the “coup de fouet” on many aspects. Without giving a final answer concerning the origin of these two phenomena, our results present some contradictions with the explanation generally accepted today. It is, also, shown that the study of these phenomena constitutes an original means to investigate the full-charge and full-discharge conditions, together with other characterization methods like impedance spectroscopy. On the other hand, results presented show that it is not possible to connect the “coup de fouet” parameters to the battery capacity without taking care of the high-SOC level, the rest time preceding the discharge, and the depth of the latter discharge, which compromises the reliability of this method suggested in several papers and patents, in particular in applications with irregular cyclings.