Collective operation protocol selection in a parallel computer that includes compute nodes may be carried out by calling a collective operation with operating parameters; selecting a protocol for executing the operation and executing the operation with the selected protocol. Selecting a protocol includes: iteratively, until a prospective protocol meets predetermined performance criteria: providing, to a protocol performance function for the prospective protocol, the operating parameters; determining whether the prospective protocol meets predefined performance criteria by evaluating a predefined performance fit equation, calculating a measure of performance of the protocol for the operating parameters; determining that the prospective protocol meets predetermined performance criteria and selecting the protocol for executing the operation only if the calculated measure of performance is greater than a predefined minimum performance threshold.