For simulating GI/G/1 queues, we investigate estimators of stationary delay-in-queue moments that were suggested but not investigated in our recent article and we develop new ones that are even more efficient. Among them are direct spread estimators that are functions of a generated sequence of spread idle periods and are combinations of estimators. We also develop corresponding conditional estimators of equilibrium idle-period moments and delay moments. We show that conditional estimators are the most efficient; in fact, for Poisson arrivals, they are exact. In simulation runs with both Erlang and hyperexponential arrivals, conditional estimators of mean delay are more efficient than a published method that estimates idle-period moments by factors well over 100 and by factors of over 800 to several thousand for estimating stationary delay variance.