Ranking of scientific periodicals by the method of citation counting provides valueable information about the degree of importance of the ranked periodicals. But such lists suffer from some inherent limitations. This paper discusses various pitfalls of traditional ranking lists and suggests, as a remedial measure, three new bibliometric parameters, namely, (1) scientific interest of a journal in relation to total number of articles published; (2) compactness of information content in a scientific periodical; and (3) scientific value of the papers in relation to compactness of presentation. It is believed that these new parameters, whenever applied to any traditional ranking list, will help to identify the accurate positions of different scientific journals of the parent list in order of their usefulness and importance. As a case study these parameters have been applied to the first ten core journals of biochemistry identified earlier and a revised reranked order of the titles presented and discussed.