Social influence can be described as power - the ability of a person to influence the thoughts or actions of others. Identifying influential users on online social networks such as Twitter has been actively studied recently. In this paper, we investigate a modified k-shell decomposition algorithm for computing user influence on Twitter. The input to this algorithm is the connection graph between users as defined by the follower relationship. User influence is measured by the k-shell level, which is the output of the k-shell decomposition algorithm. Our first insight is to modify this k-shell decomposition to assign logarithmic k-shell values to users, producing a measure of users that is surprisingly well distributed in a bell curve. Our second insight is to identify and remove peering relationships from the network to further differentiate users. In this paper, we include findings from our study.