I wouldn't worry too much about the computer reading. It's within the range I've experienced over 3 Jazzes now. My recent fill was an actual 39.2 and a recorded 43. I've got to the stage where 4 mpg over optimistic is a reasonable bench mark. I record mine faithfully on Fuelly.com on the brim to brim method. To be honest that's because I'm a bit OCD about these things. I've often thought a quick check of the computer, knock off 4 mpg, and I'd be pretty much bang on.
I have noticed that, on long journeys, the percentage that the on-line computer is out is less. There are, on this site, people with the technical know how to explain this.