Just did a project like that and charged by the hour. I did give them an estimate of how long i think it would take and it pretty much ended up within the the range.
I also used to be very against charging per hour.
But now I am working with a client who asked me to do a couple of revision to her website in order to optimize SEO, she said she liked her site the way it is but just wanted me to change some text and images. I felt that she was not clearly stating what the project requires, so I reluctantly told her I will charge her per hour. But now she just wants to also change one more little thing, make one section a bit better, etc, and boy am I glad I told her I will charge her on hourly fee!