Locating apparent horizons is not only important for a complete unders
tanding of numerically generated spacetimes, but it may also be a cruc
ial component of the technique for evolving black-hole spacetimes accu
rately. A scheme proposed by Libson, Masso, Seidel, and Suen, based on
expanding the location of the apparent horizon in terms of symmetric
trace-free tensors, seems very promising for use with three-dimensiona
l numerical data sets. In this paper, we generalize this scheme and pe
rform a number of code tests to fully calibrate its behavior in black-
hole spacetimes similar to those we expect to encounter in solving the
binary black-hole coalescence problem. An important aspect of the gen
eralization is that we can compute the symmetric trace-free tensor exp
ansion to any order. This enables us to determine how far we must carr
y the expansion to achieve results of a desired accuracy. To accomplis
h this generalization, we describe a new and very convenient set of re
currence relations which apply to symmetric trace-free tensors.