The Hirsch index or h-index is widely used to quantify the impact of an individual's scientific research output, determining the highest number h of a scientist's papers that received at least h citations. Fractionalised counting of the publications is an appropriate way to distribute the impact of a paper among all the coauthors of a multi-authored manuscript in an easy way, leading to a simple modification hm of the h-index. On the other hand the exclusion of self-citations allows one to sharpen the index, what is appropriate, because self-citations are usually not reflecting the significance of a publication. I have previously analysed the citation records of 26 physicists discussing the sharpened index hs as well as the modification hm of the original h-index. In the present investigation I combine these two procedures yielding the modified sharpened index hms. For a better comparison, interpolated indices are utilized. The correlations between the indices are rather strong, but nevertheless the positions of some datasets change, in a few cases significantly, depending on whether they are put into order according to the values of h, hm, hs, or hms. This leads to the conclusion that the additional effort in determining the modified sharpened index hms is worth performing in order to obtain a fairer evaluation of the citation records.