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A balloon observation at 3.5 g cm−2 over Minneapolis on June 10, 1962, has resulted in upper limits from the quiet sun of less than 0.05 count cm−2 sec−1 over the range 160 to 800 kev. This limit is considerably below those previously available. The detector consisted of a 3.4-cm diameter by 5.4-cm NaI crystal surrounded, except for a 1-ster forward aperture, by a 14.6-cm diameter and 20 cm long CsI collimating shield connected in active anticoincidence. The detector was servo-controlled to observe the sun, 180° in azimuth from the sun, as well as vertical, horizontal, and downward. The differences between the rates pointing to and away from the sun give upper limits for the solar flux at a 95% confidence level of 0.058, 0.048, 0.050, and 0.043 count cm−2 sec−1 Mev−1 over the 163–325, 325–488, 488–651, and 651–774 kev range, respectively. Since the Crab Nebula was in the detector aperture during the flight, these upper limits also apply to that object. Correction for the counter efficiency will give upper limits for the true flux somewhat higher than the above numbers, depending on the shape of the photon spectrum. Observation of the diffuse background γ-ray spectrum over this range due to cosmic-ray interactions in the atmosphere gave a result of 0.72 count cm−2 sec−1 ster−1 Mev−1 around 300 kev, in general agreement with Peterson's previous results. The atmospheric line at 0.5 Mev due to positron annihilation was resolved. A γ-ray line at 660 kev was also detected and was determined to be due to Cs137 from fallout debris. The implied activity is 8±2×10−3 disintegrations per g sec, averaged from 70,000 to 128,000 feet. Additional information pertinent to the application of this detector system to γ-ray astronomy was obtained.