Very-fast-compression, hot-ion, high-β theta pinches are sometimes hydrodynamically stable,in spite of slight unfavourable field-line curvature. This phenomenon cannot be explained quantitatively by conventional finite-ion-Larmor-radius theory since the orbits are larger than the diameters of the plasmas considered. Therefore, an idealized, collisionless "bounce" model (elastic ion reflections from a negligibly thin sheath) with the magnetic field totally excluded from the bulk of the plasma is assumed for analysis. The ion trajectories are then calculated for slowly growing flute perturbations of the interface. It is found that ions having angles of incidence near 0, π/m, ..., (½m-l)π/m for even mode numbers м, or near π/2m, 3π/2m, ..., (m-l)π/2m for odd m become trapped and reflected only from the flute indentations. Therefore, a strong restoring force results if the initial velocity distribution contains a sufficient density of ions at one of these critical angles. In particular, radially concentrated distributions are always stabilizing for m = 2. Moderately concentrated distributions are also stabilizing for m = 3, but this mode is unstable for stronger radial concentration.