New Mexico is the land of wide open spaces and free ranging cattle, a land made for coursing, both lure and live game. New Mexico has a history of coursing dating back to the time of the Spanish Conquistadors as they brought with them their Greyhounds to hunt game in the New World. The first mention of the use of coursing dogs appears in the journals of Bernal Diaz, who chronicled the Cortez expedition. It seems that a greyhound, name unknown, was busily hunting game when the time for the return to the ship arrived. When the hound could not be caught, Grijalva, the contingent's leader, ordered the errant hound left behind. The hound was joyfully reunited with the explorers at a later date, as recounted by the historian Gomara, She greeted them wagging her tail, jumping from one to the other, and later went into the woods that were near and returned bringing hares and rabbits.

Other stories of New Mexico surround the particular adventures of Charles F. Lummis. In September 1884, Lummis left Cincinnati, Ohio to make a "Tramp Across the Continent" (title of his later book). He completed his trek in 143 days, covering 3507 miles, many of the miles shared only by his greyhound, Shadow. Lummis found Shadow as an abandoned pup near Pueblo, Colorado. They traveled the state, far and wide, one night meeting up with a cougar on a narrow mountain trail. They crossed New Mexico and Arizona, reaching the Mojave desert before a tragedy took Shadow's life.

Coursing hounds were kept by an assortment of ranchers in New Mexico for years to hunt coyotes and wolves to help protect their flocks and herds. Farmers and vintners kept hounds to course jackrabbits which decimated crops and vineyards.