Here on St Barts Island, we have a number of different Villa Rental Agencies.  One is Caraibes Welcome Center.  Although I do not know much about them, they seem to have both car rentals and villa rentals.  It seems their approach is to take your request, and then match you up with a villa.  They have a few villas listed on their website, but they also hint about having others to choose from, although they don’t specify what those are.  Positioned as an "information and reservation center," their website says:

Tell us when you want to come, your budget, and what sort of accommodations you prefer, and we’ll reply promptly with suggestions tailored to your needs. 

Not 100% sure what they’re all about, but I’m working on finding out, and when I have more details, I’ll let you all know!!