Place the lime juice, the olive oil, the garlic, the salt and oregano in a large resealable plastic bag. Shake the sealed bag until ingredients are well mixed. Taste the marinade for tartnessand if too tart, add a little more oil. If there isn't enough zing add more lime. The garlic and salt flavors should also be up frontand not overpowering. Place tenderloins in the bag, seal, and turn to the coating. Let marinate in the refrigerator for 2 to 5 hours. Preheat the grill to medium heat.
Lightly oil the grill grate and discard marinade. Grill the tenderloins for 20 to 30 minutes and turn them once.