The factors governing word order in binomials, i.e. coordinated word pairs of the same word class, have been the subject of discussion for a long time in linguistics. For example, why do we say law and order but not order and law? The article tests seventeen different potential ordering constraints that have previously been suggested, from the areas of semantics, phonology and word frequency, by checking over 500 high-frequency binomials extracted from the BNC against them. A clear hierarchy of constraints is suggested following the analysis of their success in predicting binomial order. In addition, however, attention is drawn to the reversibility status of binomials. The vast majority of English binomials is reversible to a smaller or larger degree. Reversibility scores were computed for all binomials in the sample so that the relationship between reversibility on the one hand and the adherence to the ordering constraints on the other could be analysed, finding that a number of semantic and metrical ordering constraints indeed increase their predictive success towards the frozen end of the reversibility cline. Complying with these constraints, then, increases the likelihood of a binomial to be less reversible. Claims for the influence of certain factors on the freezing process are thus substantiated for the first time.