Monogamy is associated with sibling-directed altruism in multiple animal taxa, including insects, birds and mammals. Inclusive-fitness theory readily explains this pattern by identifying high relatedness as a promoter of altruism. In keeping with this prediction, monogamy should promote the evolution of voluntary sterility in insect societies if sterile workers make for better helpers. However, a recent mathematical population-genetics analysis failed to identify a consistent effect of monogamy on voluntary worker sterility. Here, we revisit that analysis. First, we relax genetic assumptions, considering not only alleles of extreme effect-encoding either no sterility or complete sterility-but also alleles with intermediate effects on worker sterility. Second, we broaden the stability analysis-which focused on the invasibility of populations where either all workers are fully sterile or all workers are fully reproductive-to identify where intermediate pure or mixed evolutionarily stable states may occur. Third, we consider a broader range of demographically explicit ecological scenarios relevant to altruistic worker non-reproduction and to the evolution of eusociality more generally. We find that, in the absence of genetic constraints, monogamy always promotes altruistic worker sterility and may inhibit spiteful worker sterility. Our extended analysis demonstrates that an exact population-genetics approach strongly supports the prediction of inclusive-fitness theory that monogamy promotes sib-directed altruism in social insects.