Consensus is one of the key problems in fault tolerant distributed computing. A very popular model for solving consensus is the failure detector model defined by Chandra and Toueg. However, the failure detector model has limitations. The paper points out these limitations, and suggests instead a model based on communication predicates, called HO model. The advantage of the HO model over failure detectors is shown, and the implementation of the HO model is discussed in the context of a system that alternates between good periods and bad periods. Two definitions of a good period are considered. For both definitions, the HO model allows us to compute the duration of a good period for solving consensus. Specifically, the model allows us to quantify the difference between the required length of an initial good period and the length of a non initial good period.