  We study search trees with 2-way comparisons (2WCST's), which involve
separate less-than and equal-to tests in their nodes, each test having two
possible outcomes, yes and no. These trees have a much subtler structure than
standard search trees with 3-way comparisons (3WCST's) and are still not well
understood, hampering progress towards designing an efficient algorithm for
computing minimum-cost trees. One question that attracted attention in the past
is whether there is an easy way to determine which type of comparison should be
applied at any step of the search. Anderson, Kannan, Karloff and Ladner studied
this in terms of the ratio between the maximum and total key weight, and
defined two threshold values: $\lambda^-$ is the largest ratio that forces the
less-than test, and $\lambda^+$ is the smallest ratio that forces the equal-to
test. They determined that $\lambda^- = 1/4$, but for the higher threshold they
only showed that $\lambda^+\in [3/7,4/9]$. We give the tight bound for the
higher threshold, by proving that in fact $\lambda^+ = 3/7$.
