An elegant approach to learning temporal orderings from texts is to formulate this problem as a constraint optimization problem, which can be then given an exact solution using Integer Linear Programming. This works well for cases where the number of possible relations between temporal entities is restricted to the mere precedence relation [Bramsen et al., 2006; Chambers and Jurafsky, 2008], but becomes impractical when considering all possible interval relations. This paper proposes two innovations, inspired from work on temporal reasoning, that control this combinatorial blow-up, therefore rendering an exact ILP inference viable in the general case. First, we translate our network of constraints from temporal intervals to their endpoints, to handle a drastically smaller set of constraints, while preserving the same temporal information. Second, we show that additional efficiency is gained by enforcing coherence on particular subsets of the entire temporal graphs. We evaluate these innovations through various experiments on TimeBank 1.2, and compare our ILP formulations with various baselines and oracle systems.