Among other things, Trace takes a countfuncs (Boolean) value to turn on listing of the functions as the code is run.
t = TestExec()
trace = Trace(countfuncs=True)
try:
trace.run('t.run_this_and_that()')
print "COUNTFUNCS"
except NameError:
print NameError
<type 'exceptions.NameError'>
COUNTFUNCS
Interestingingly, it seems to have disabled the trace. Not what I was expecting.