Alternating Dat-Nom/Nom-Dat verbs in Icelandic are notorious for instantiating two diametrically opposed argument structures: the Dat-Nom and the Nom-Dat construction. We conduct a systematic study of the relevant verbs to uncover the factors steering the alternation. This involves a comparison of 15 verbs, five alternating ones, and as a control, five Nom-Dat verbs and five non-alternating Dat-Nom verbs. Our findings show that alternating verbs instantiate the Nom-Dat construction 54% of the time and the Dat-Nom construction 46% of the time on average for four of five verbs when both arguments are full NPs. However, in configurations with a nominative pronoun, the Nom-Dat construction takes precedence over the Dat-Nom construction. Also, for the double-NP configuration, a logistic regression analysis identifies indefiniteness and length as two key predictors, apart from nominative case marking. We demonstrate that the latter systematically correlates with discourse-prominence, which we show, upon closer inspection, correlates with topicality.