We report on ion beams injected into the plasma sheet boundary layer (at or near the separatrix) at distances >39 RE and up to 169 RE that bounced several times back and forth (up to three echoes) while remaining in coherent bunches before thermalizing in the central plasma sheet. These bouncing ion clusters (BIC) interacted with the far-tail current sheet with a possible curvature parameter, $kappa$, of less than 2. The existence of these BIC shows that ion beams can interact several times nonadiabatically with the far-tail current sheet and still remain coherent. Owing to the large-scale E ¿ B drift, echoes also appeared in the central plasma sheet (CPS) after several bounces. The echoes had higher energies compared with the initially injected ion cluster which can be attributed to additional nonadiabatic acceleration during their second and third interaction with the tail current sheet. After multiple bounces, the ion cluster became thermalized isotropic plasma mixing with the CPS. The three BIC events presented here were identified on the basis of the energy dispersion slopes associated with the ions. Simple model calculations showed, however, that in the case of these far-tail ion injections the 1:3:5:etc.-ratios of travel distances for echoes, used as diagnostics for near-Earth adiabatic BIC, are not valid. This is largely due to a significant shortening of the tail field lines, caused by earthward convection, during the large ion travel times. The model calculations also reproduced newly observed properties such as concave dispersion slopes for the echoes. Furthermore, we argue here that the energy dispersion of the BIC was dominated by a time-of-flight effect. The injection region for the three BIC events, determined on the basis of this time-of-flight interpretation, covered broad ranges of ΔX (GSE) = 26--40 RE. Two BIC events occurred during the substorm recovery phase; the other BIC event occurred during quiet geomagnetic activity. For two BIC events, UV images were available showing that they were magnetically connected to the poleward arc of the double oval. One BIC event was also conjugate to a small active region inside the poleward arc. We conclude that these nonadiabatic BIC are different from the adiabatic BIC that are routinely reported in the CPS.