Assessing global interrater agreement is difficult as most published indices are affected by the presence of mixtures of agreements and disagreements. A previously proposed method was shown to be specifically sensitive to global agreement, excluding mixtures, but also negatively biased. Here, we propose two alternatives in an attempt to find what makes such methods so specific. The first method, R_B, is found to be unbiased while at the same time rejecting mixtures, is detecting agreement with good power and is little affected by unequal category prevalence as soon as there are more than two categories.