Emacs - Changing show-paren-mode Areas

I like show-paren-mode in Emacs, but I would really like to change the highlighting behavior for closing brackets. That is, I want the opening bracket to be highlighted when the point is on the closing bracket. The default behavior highlights the opening bracket when the point is on the character following the closing bracket. Is this easy to change? Also, I would be interested in potential benefits of keeping the show-paren-mode behavior as it is.