Random grid path generator

I have a grid consisting of passable and non-passable squares, and need to randomly generate a path. It needs to be something between a maze and a pac-man style map so it has multpile routes between the start and the end and be relatively open but still has dead ends. I've done some research and all I can find is a randomised depth-first search which would make a perfect maze, which I don't want. Here's an example of the sort of path needed: