This paper studies consecutive-2 systems on trees. We show that given a set of probability values, the optimal assignment for binary trees depends on the particular values, whereas for k−regular trees, which are closely related to binary trees, it depends only on their relative ordering. In our proof, we introduce the notion of first-term-invariance, which might have further applications. We also show that the problem of computing the failure probability of consecutive-2 system is #P-complete in general, though the problem on trees is shown to be strongly polynomial.