Actually Jouri - if you have your own individual funding it is possible to pursue your own project if it fits into your chosen supervisor's genreal remit. When I was applying, I had a short chat with my supervisor and suggested some project ideas that intersted me. (It had been made very clear that I would be responsible for coming up with my own project.) He had a definite preference for one, so I expanded that into a funding proposal, which he signed as the potential supervisor. This is not that uncommon, especially in fields that don't require a lot of research costs.