Solar‐cosmic‐ray‐produced Ne (SCR ‐Ne), in the form of low cosmogenic 21Ne/22Ne ratios (21Ne/22Necos <0.8), is more likely to be found in rare meteorite classes, like Martian meteorites, than in ordinary chondrites. This may be the result of a sampling bias: SCR ‐Ne is better preserved in meteorites with small preatmospheric radii and these specimens are often only studied if they belong to unusual or rare classes. We measured He and Ne isotopic concentrations and nuclear tracks in 25 small unpaired ordinary chondrites from Oman. Most chondrites have been intensively heated during atmospheric entry as evidenced by the disturbed track records, the low 3He/21Ne ratios, the low 4He concentrations, and the high peak release temperatures. Concentration depth profiles indicate significant degassing; however, the Ne isotopes are mainly undisturbed. Remarkably, six chondrites have low 21Ne/22Necos in the range 0.711–0.805. Using a new physical model for the calculation of SCR production rates, we show that four of the chondrites contain up to ~20% of SCR‐Ne; they are analyzed in terms of preatmospheric sizes, cosmic ray exposure ages, mass ablation losses, and orbits. We conclude that SCR‐Ne is preserved, regardless of the meteorite class, in specimens with small preatmospheric radii. Sampling bias explains the predominance of SCR‐Ne in rare meteorites, although we cannot exclude that SCR‐Ne is more common in Martian meteorites than it is in small ordinary chondrites.