Administering connection identifiers for collective operations in a parallel computer, including prior to calling a collective operation, determining, by a first compute node of a communicator to receive an instruction to execute the collective operation, whether a value stored in a global connection identifier utilization buffer exceeds a predetermined threshold; if the value stored in the global ConnID utilization buffer does not exceed the predetermined threshold: calling the collective operation with a next available ConnID including retrieving, from an element of a ConnID buffer, the next available ConnID and locking the element of the ConnID buffer from access by other compute nodes; and if the value stored in the global ConnID utilization buffer exceeds the predetermined threshold: repeatedly determining whether the value stored in the global ConnID utilization buffer exceeds the predetermined threshold until the value stored in the global ConnID utilization buffer does not exceed the predetermined threshold.