Fluorescence lifetime imaging (FLIM) allows the quantification of sub-cellular processes in situ, in living cells. A number of approaches have been developed to extract the lifetime from time-domain FLIM data, but they are often limited in terms of speed, photon efficiency, precision or the dynamic range of lifetimes they can measure. Here, we focus on one of the best performing methods in the field, the centre-of-mass method (CMM), that conveys advantages in terms of speed and photon efficiency over others. In this paper, however, we identify a loss of photon efficiency of CMM for short lifetimes when background noise is present. We subsequently present a new development and generalization of CMM that provides for the rapid and accurate extraction of fluorescence lifetime over a large lifetime dynamic range. We provide software tools to simulate, validate and analyse FLIM data sets and compare the performance of our approach against the standard CMM and the commonly employed least-square minimization (LSM) methods. Our method features a better photon efficiency than standard CMM and LSM and is robust in the presence of background noise. The algorithm is applicable to any time-domain FLIM data set.