In the first EGRET catalog, upper limits were given for selected objects not detected during the Phase 1 all-sky survey. These upper limits are determined using the likelihood calculation and depend on the EGRET exposure to a given direction, the contribution of the diffuse gamma radiation, and the proximity and strength of detected sources. Similar upper limits have been determined for the Phase 1 + Phase 2 summed exposure. Instead of using specific sources, these upper limits have been calculated for a 1
x 1
grid on the sky. The result is shown in Figure 4, where the upper limit is a 95% confidence limit in units of photons (E > 100 MeV) cm
s
. For comparison with this figure, the faintest source in the catalog with a significance 
> 4 has a flux of (6.2 
1.7) x 10
cm
s
.
The sources in the EGRET catalog have been considered in this calculation. As noted above, EGRET cannot easily resolve sources within 1
of each other, and the point spread function of EGRET is large enough to influence sources several degrees away. For this reason, upper limits near catalog sources may be underestimated. For any object within 1
of a catalog source (especially an unidentified source), it is recommended that the source flux itself be taken as a conservative upper limit.