The current leading paradigm for temporal information extraction from text consists of three phases: (1) recognition of events and temporal expressions, (2) recognition of temporal relations among them, and (3) time-line construction from the temporal relations. In contrast to the first two phases, the last phase, time-line construction, received little attention and is the focus of this work. In this paper, we propose a new method to construct a linear time-line from a set of (extracted) temporal relations. But more importantly, we propose a novel paradigm in which we directly predict start and end-points for events from the text, constituting a time-line without going through the intermediate step of prediction of temporal relations as in earlier work. Within this paradigm, we propose two models that predict in linear complexity, and a new training loss using TimeML-style annotations, yielding promising results.