I also like Tess Gerritsen, and dislike very gruesome books.
I really like Phil Rickman's books. Amongst others he's written a series of suspense novels set on the England / Wales border. They feature a female Anglican priest called Merrily Watkins, who is also the exorcist for the diocese. The cases she investigates are kept very low key - nothing that crosses the line from suspense to horror - and they're real page turners.