The "Reason" you will find it nearly impossible to get a rental car in December, is that every Dominican in the WORLD comes "Home" in December!
Also, be advised, they will all be drunk and driving in those rental cars.
If you do find a car. it may not be there when you arrive.
They give you a reservation, but if someone comes first with $$$$$$$$$$$$$$$$$ they get the car.
Also, get the additional insurance, and note ANY scratches, dings, bumps, and blemishes on the contract BEFOR you leave the lot. Take pictures if you can.
AND, when you take the car back be ready to fight about any "so-called" damages they want you to pay for.
Welcome to "Paradise", Dominican Style!!!!!!!!!!!!!
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