Temporal Constraint Satisfaction Problems (TCSP) is a well known approach for representing and processing temporal knowledge. Important properties of the knowledge can be inferred by computing the minimal networks of TCSPs. Consistency and feasible values are immediately obtained; computing solutions can be assisted. Yet, in general, computing the minimal network of a disjunctive TCSP is intractable. The minimal network approach requires computation of the full network in order to answer a query. In this paper we characterize TCSPs for which subsets of the minimal network can be computed without having to compute the whole network. The partial computation is enabled by decomposition of the problem into a tree of sub-problems that share at most pairs of time points. Such decompositions are termed sim/2-tree decompositions. For TCSPs that have sim/2-tree decompositions, minimal constraints of input propositions can be computed by independent computations of the minimal networks of the s...