This paper extends the notion of time delay into a threefold concept. Based on this renewed definition, a novel strategy for time delay estimation (TDE) that leads to a model with optimal fit is presented. Its goal is to find the best time delay, so that a given model structure with a certain order and adjusted for an identification dataset best represents the true system. Such optimization strategy is said to be fit-driven, since it maximizes the fit index. A brief review of classical TDE techniques is presented and the problem of TDE is further inspected from a system identification perspective. Model quality (in the fit sense) is measured and compared in Monte Carlo simulations, using identified models with TDE derived from both classical and the proposed techniques.