Using new and archival observations made with the Swift satellite and other facilities, the authors examine 147 X-ray sources selected from the ROSAT All-Sky-Survey Bright Source Catalog (RASS/BSC) to produce a new limit on the number of isolated neutron stars (INSs) in the RASS/BSC, the most constraining such limit to date. Independent of X-ray spectrum and variability, the number of INSs is <= 48 (90% confidence). Restricting attention to soft (kT_eff < 200 eV), non-variable X-ray sources - as in a previous study - yields an all-sky limit of <= 31 INSs. In the course of their analysis, the authors identify 5 new high-quality INS candidates for targeted follow-up observations. A future all-sky X-ray survey with eROSITA, or another mission with similar capabilities, can be expected to increase the detected population of X-ray-discovered INSs from the 8 - 50 in the BSC, to (for a disk population) 240 - 1500, which will enable a more detailed study of neutron star population models. Following selection of the INS candidates, short (~ 1 ks) follow-up observations with Swift/XRT were obtained for 92 of the candidates; these observations decreased the X-ray positional uncertainty (the systematic positional error associated with Swift blind pointing observations is on the order of 3.5"). The authors obtained (where possible) contemporaneous UV observations with Swift/UVOT for counterpart identification with off-band objects. This table was created by the HEASARC in May 2012 based on <a href="https://cdsarc.cds.unistra.fr/ftp/cats/J/ApJ/714/1424">CDS Catalog J/ApJ/714/1424</a> files table1.dat and table2.dat. This is a service provided by NASA HEASARC .