The Coherent Approximation Principle (CAP) is a method for aggregating forecasts of probability from a group of judges by enforcing coherence with minimal adjustment. This paper explores two methods to further improve the forecasting accuracy within the CAP framework and proposes practical algorithms that implement them. These methods allow flexibility to add fixed constraints to the coherentization process and compensate for the psychological bias present in probability estimates from human judges. The algorithms were tested on a data set of nearly half a million probability estimates of events related to the 2008 U.S. presidential election (from about 16000 judges). The results show that both methods improve the stochastic accuracy of the aggregated forecasts compared to using simple CAP.