Spontaneous-potential (SP) log data from wells in the deep eastern Greater Green River Basin (GGRB) suggest that what appears to be overpressured pervasive gas at high saturation in Upper Cretaceous sandstones outside conventional fields is gassy water with gas present at uneconomically low saturation. Sandstones of the Lewis Shale and Mesaverde Group within conventional-trap fields in the deep eastern GGRB exhibit normal-SP deflections, indicating saline formation water with low formation-water resistivity (R-w) that yields calculated water saturations (4) less than 50%. However, in deep-basin areas outside conventional traps, these Upper Cretaceous sandstones generally exhibit reversed-SP signatures reflecting anomalously low-salinity founation water with anomalously high R-w, that yields calculated S-w greater than 60%. Uneconomically low gas saturations are corroborated by lack of commercial gas production from reversed-SP sandstones despite (1) prominent gas shows during drilling, (2) significant overpressure, and (3) log-measured porosity and resistivity that often are indistinguishable from those observed with commercially productive normal-SP sandstones within conventional traps. Anomalously low-salinity water in deep-basin sandstones outside conventional traps is proposed to result from dilution of original saline formation water by fresh water expelled during smectite-clay conversion to illite with increasing temperature (burial depth). Low penneability of deep-basin sandstones retards escape of the added fresh water, which contributes to overpressure and to deceptively high formation resistivity. Although the upward transition to more saline formation water is gradational, mapped top of reversed SP cuts across stratigraphic boundaries, with relief exceeding 2000 ft (610 m). It is unclear whether regional continuous gas in reversed-SP sandstones has been at low saturation since the onset of gas migration or whether saturations were higher prior to the influx of fresh water. What is reasonably certain is that subsequent to gas migration, fresh-water influx in the deep basin regionally diluted original saline formation water outside conventional traps. Similar fotmation-water salinity of nounal-SP sandstones of the Lewis Shale and Mesaverde Group within deep-basin conventional traps suggests that high-saturation gas and associated irreducible saline folination water in these fields are locked-in accumulations unaffected by subsequent fresh-water influx.