The system (10) includes a guide plate (32) covering at least about fifty percent of a distance along a first or a second end edge (28, 30) between first and second side edges (24, 26) of a veterinary table (12). The plate (32) defines five or more cord positioning guides (36) per foot of extension of the guide plate (32) between the first and second table side edges (24, 26). The cord positioning guides (36) secure an animal restraint cord (38) against movement toward the first or second table side edges (24, 26). The cord (38) is secured at one end to a limb (48) of a small animal (22) such as a dog, extends through one of a variety of cord positioning guides (36), and is secured against movement toward the animal (22) by a cord securing apparatus (52).