During his time as a lawyer, Graves was also a justice of the peace and acted as trial commissioner for the Paducah Police Court and the McCracken County Quarterly Court.[2] After practicing law for 20 years, Graves was elected first as a circuit judge and then as a district judge in McCracken County.[2] After Justice Thomas B. Spain announced his retirement from the Kentucky Supreme Court in June 1995, Graves announced he would resign his position to seek Governor Brereton Jones's appointment to fill the vacancy and would be a candidate in the special election for the balance of Spain's term, which would not expire until January 1999.[3][5] Jones appointed retired circuit court judge William Fuqua to fill the vacancy, but Fuqua said he would not be a candidate in the special election.[6] Graves was one of six candidates in the special election for the remainder of Spain's term.[5] With 15,496 votes, he finished about 650 votes ahead of his nearest challenger, Charles W. Boteler Jr.; the remaining candidates were Will Shadoan (14,581 votes), Rick Johnson (14,490 votes), Richard Hayes Lewis (12,338 votes) and Christopher "Kit" Hancock (5,013 votes).[7]
At the expiration of Spain's unexpired term, Graves announced he would seek re-election.[8] Rick Johnson, a justice of the Kentucky Court of Appeals and a challenger from the 1995 special election, also sought the seat.[8] Graves won the rematch for a full, eight-year term by 2,200 votes.[9]
In 2004, Graves announced he would not seek another term on the court, but later changed his mind.[10] For the third time in as many elections, Johnson was one of Graves' opponents, along with Circuit Judge Bill Cunningham.[10] Graves refused to accept campaign donations, and in March 2006, just ahead of the nonpartisan May primary, he announced he would withdraw from the race, citing an unwillingness to invest enough time and money to make a competitive race.[9]