For the purpose of making inferences for a one-dimensional interest pa
rameter, or constructing approximate complementary ancillaries or resi
duals, the directed likelihood or signed square root of the likelihood
ratio statistic can be adjusted so that the resulting modified direct
ed likelihood is under ordinary repeated sampling approximately standa
rd normal with error of O(n(-3/2)), conditional on a suitable ancillar
y statistic and hence unconditionally. In general, suitable specificat
ion of the ancillary statistic may be difficult. We introduce two adju
sted directed likelihoods which are similar to the modified directed l
ikelihood but do not require the specification of the ancillary statis
tic. The error of the standard normal approximation to the distributio
n of these new adjusted directed likelihoods is O(n(-1)), conditional
on any reasonable ancillary statistic, which is still an improvement o
ver the unadjusted directed likelihoods.