Stratified telephone sample designs have been proposed which provide samples of phone numbers that have high concentrations of working residential telephone numbers but require little replacement sampling. These designs use commercial lists of telephone numbers to create sampling strata based on counts of listed residential numbers. Disproportionate allocation of sample size to strata composed of banks with listed numbers and to strata of banks without listed numbers has been considered as a means of increasing design efficiency. This paper uses recent empirical results to improve the specification of optimal stratified sample designs in different survey contexts. In particular, an informed discussion of sampling from banks without listed numbers (so-called "low-density" strata) is given.