We study the class of tree-growing search strategies introduced by
Lent and Mahmoud, searches for which data are stored in a deterministic
sequence of tree structures (e.g., linear search in forward order).
Specifically, we study the conditions under which the number of comparisons
needed to sort a sequence of randomly ordered numbers is asymptotically normal.
Our main result is a sufficient condition for normality in terms of the growth
rate of tree height alone; this condition is easily computed and is satisfied
by all standard deterministic search strategies. We also give some examples of
normal search strategies with surprisingly small variance, in particular, much
smaller than is possible for the class of consistent strategies that are the
focus of the work by Lent and Mahmoud.