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A mean containment time τ of many seconds has been observed for a significant fraction of the energetic (≤ 2.2-MeV) positrons emitted from Ne19 isotropically and uniformly in a mirror geometry with mirror ratio R in the range 1.1–3.7. Long-time containment has been observed for particles that escape through a mirror at radial distances for which the particle orbits do not encircle the axis, as well as for those that escape on or near the axis. The dependence of τ on the Z of the scattering gas, the gas pressure, the positron energy, the coil current, and the diameter and separation of the coils has been investigated. Most of the data were obtained with the two mirror coils separated one coil mean diameter. For sufficiently small values of λ (the ratio of the maximum orbit diameter on axis to the coil mean diameter), τ is independent of λ and its dependence upon the above parameters agrees with the predictions of scattering theory. Also, the fraction of particles trapped as a function of the mirror ratio agrees with calculations based on the loss cone concept. These results demonstrate that the particles ``behave adiabatically'' if λ is less than about 1/10. For larger values of λ the observed τ's are shorter. Results obtained with probes are in agreement with the prediction that the intersections of particle drift surfaces with the plane midway between the mirror coils are concentric circles centered on the axis. In the cusped field resulting from opposite currents in two coils separated by one coil mean radius, containment times of several seconds have been observed at radial distances where the field is of sufficient strength that ``adiabatic behavior'' is expected. Near the axis, however, no long-time (> 0.5-sec) containment has been observed.