An animal toy includes structure presenting regions having characteristics providing different degrees of animal interest and/or accessibility, such that there is a higher likelihood that a dog will retain a particular part of the toy in its mouth apart from another region intended for grasping by the owner. The toy finds application in various modes of play, including tug activities between dog and owner, throwing and retrieval, and any other type of interaction in which the toy is held by the dog in its mouth and is thereby subjected to a depositing of saliva over the particular involved region of the toy. An embodiment includes members which include animal access regions and which are disposed in circumferentially spaced apart positions about a toy axis and radially spaced apart therefrom, and at least partially shielded handles, portions of which are positioned radially inward of a outermost radial extent of said members. Exposure to saliva by a user is reduced by avoided contact with the region accessed to a greater degree by the animal during play.