Statistical uncertainties in emission computed tomography were simulated in 60 computer studies involving various numbers of events and distributions of activity. Previous studies have shown that for a uniform disc of activity of rms percentage of uncertainty per resolution cell is: 120 X (number of resolution cells)1/4 X (number of events per resolution cell)- 1/2. In this work we examined the more general situation where one or two regions of uniform activity are surrounded by a uniform background, and found that for an equal number of recorded events the uncertainties were reduced when the activity was concentrated in a portion of the field. The empirical relation rms % uncertainty in nt = 120(N)1/4(nt)-3/4, where nt is the number of events in an average target (organ) resolution cell and N is the total number of events recorded, satisfactorily described the relationships between uncertainties, contrast, total number of detected events, and number of resolution cells for all 60 computer studies. By means of this relation, we show the theoretical possibility of gated cardiac imaging with 20% uncertainty in 1 cm X 1 cm regions, and of 1-sec cerebral blood-flow images with 20% uncertainty in 2 cm X 2 cm regions.