We report measurements of Al-26 and Be-10 activities in nine ordinary chondrites and of the light noble gas concentrations and Cl-36 and Ca-41 activities in subsets of those meteorites. All but Murray have low Ne-21 concentrations (<1.0 x 10(-8) cm(3) STP/g) and have previously been used to estimate Ne-21 production rates. Ladder Creek, Murchison, Sena, and Timochin have inventories of cosmogenic radionuclides that are compatible with a single stage of irradiation and give Ne-21 production rates that are consistent with the standard L-chondrite value of similar to 0.33 x 10(-8) cm(3) STP/g/Ma. In contrast, Cullison, Guenie, Shaw, and Tsarev experienced complex irradiation histories. They and several other meteorites with low nominal exposure ages also have lower He-3/Ne-21 ratios than expected based on their Ne-22/Ne-21 ratios. A general association between low Ne-21 contents and He-3 losses suggests that meteorites with short lifetimes often occupy orbits with small perihelia. However, meteorites with low Ne-21 contents, one-stage exposure histories, and losses of cosmogenic He-3 are rare. Possible explanations for the scarcity are (1) statistical, (2) that it is harder for more deeply buried protometeoroids to lose gas in a liberating collision, and (3) that it is harder to insert more deeply buried protometeoroids directly into orbits with small perihelia.