An emergency shutdown system for high-temperature gas-cooled pebble-bed reactors is proposed in addition to the common absorber rod shutdown system. This system is based on the strongly absorbing effect of small boronated graphite spheres (called KLAK), which trickle in case of emergency by gravity from the top reflector into the reactor core. The inner reflector of the Siemens-Argonaut reactor was substituted by an assembly of spherical Arbeitsgemeinschaft Versuchsreaktor fuel elements, and the shutdown effect was examined by installing well-defined KLAK nests inside this assembly. The purpose was to develop and prove a calculational procedure for determining criticality values for assemblies of large fuel spheres and small absorbing spheres.