Dynamically reconfigurable architectures or systems are able to reconfigure their function and/or structure to suit changing needs of a computation during run time. The increasing flexibility of modern dynamically reconfigurable systems improves their adaptability but also makes fast reconfiguration difficult because of the large amount of necessary reconfiguration information. However, even when a computation uses this flexibility it will not use it all the time. Therefore, we propose to make the potential for reconfiguration itself reconfigurable. This allows for speeding up reconfiguration operations during phases where only parts of the total flexibility are required. Such architectures are called hyperreconfigurable and use two types of reconfiguration operations: hyperreconfigurations for changing the reconfiguration potential and ordinary reconfigurations for actually configuring a new context for a computation.