This paper examines the issue of coercive journal self citations and the practical usefulness of two recent journal performance metrics, namely the Eigenfactor score, which may be interpreted as measuring “Journal Influence”, and the Article Influence score, using the Thomson Reuters ISI Web of Science (hereafter ISI) data for 2009 for the 200 most highly cited journals in each of the Sciences and Social Sciences. The paper also compares the two new bibliometric measures with two existing ISI metrics, namely Total Citations and the 5-year Impact Factor (5YIF) (including journal self citations) of a journal. It is shown that the Sciences and Social Sciences are different in terms of the strength of the relationship of journal performance metrics, although the actual relationships are very similar. Moreover, the journal influence and article influence journal performance metrics are shown to be closely related empirically to the two existing ISI metrics, and hence add little in practical usefulness to what is already known, except for eliminating the pressure arising from coercive journal self citations. These empirical results are compared with existing results in the bibliometrics literature.