In 1982, Morris was convicted of cocaine trafficking and was sentenced to 20 years imprisonment, with a mandatory 15-year term. In 1986, his conviction was overturned by the Florida Supreme Court because evidence he had offered to prove his entrapment defense had been excluded under a mistaken characterization as hearsay.

His 1982 conviction on cocaine trafficking charges was overturned, and he became a motivational speaker urging people to avoid drugs.

Part of a talented backfield triumvirate that also included Larry Csonka and Jim Kiick, he helped lead Miami to two Super Bowls and an undefeated season.