The BSP model can be extended with a zero cost synchronization mechanism, which can be used when the number of messages due to receives is known. This mechanism, usually known as“oblivious synchronization” implies that different processors can be in different supersteps at the same time. An unwanted consequence of this software improvement is a loss of accuracy in prediction. This paper proposes an extension of the BSP complexity model to deal with oblivious barriers and shows its accuracy.