Torsional oscillators (ϳ90 kHz) have been used between 0.06 and 100 K to study low-energy excitations in strained alkali-halide hosts doped with KCN in the concentration range from 0.2 to 5 mol %. The tunneling model, originally developed to describe the low-temperature thermal and elastic anomalies in amorphous solids, has been found to describe our data very well. From the observation that the tunneling strength varies linearly with the KCN concentration, we conclude that random internal stresses in the hosts, rather than interactions between the dopant ions, lead to the tunneling states. Implications for the origin of the tunneling states in amorphous solids and in highly disordered crystals, and also for their universality are considered.