Covariance models (CMs), as defined by Sean Eddy, do not reward insertions of valid base-pairs or complete sub-structures relative to the one consensus secondary structure. Nevertheless, some families, e. g. tRNA, contain minorities with additional informative sub-structures, which are crashed by the majority during formation of one consensus secondary structure.
Ambivalent Covariance Models (aCMs) are our prototypic suggestion to extend CMs with more than one consensus structure.