[3] Graham fought American and future NBA World Flyweight Champion Frankie Genaro On July 7, 1924, in Rochester, New York, to a draw.

[4][5] On May 17, 1926, he met Genaro for a third time at New York's Madison Square Garden in the first of three feature bouts and defeated him in a speedy ten round points decision.

Before a capacity crowd of 18,000, Graham used his longer reach, and slight extra weight to advantage against New York's former American flyweight champion.

[3][6][7] On September 8, 1924, fighting as Mickey Garcia in a ten-round semi-final, he defeated Jackie Snyder in a disqualification, 1:35 into the eighth round at Queensboro Athletic Club in Queens, New York.

[8] He defeated Jewish boxer Nat Pincus in a technical knockout, 1:03 into the eighth round on January 9, 1925, at New York's Madison Square Garden.

[11] On July 23, 1925, Graham defeated Abe Goldstein, a 1923 NYSAC World Bantamweight Champion, in an exciting eight round points decision at the Velodrome in New York City.

[15][16] August 5, 1926, at New York's Madison Square Garden, Graham scored a technical knockout over Dominick Petrone due to a dislocated right shoulder he complained of :45 seconds into the eighth round.

[3][17] On September 2, 1926, he defeated top rated bantamweight Chick Suggs in a ten-round points decision at Madison Square Garden.

[18] Graham danced through the ten rounds, showing his best technique against his undefeated opponent, and nearly gaining a knockout in the ninth, though Suggs fought on and remained on his feet throughout the bout.

[19][20] Breaking a long winning streak, on December 17, 1926, he fought future triple weight class world champion Tony Canzoneri at Madison Square Garden in a non-title match and lost by a ten-round points decision.

[21] On February 4, 1927, Graham first gained the opportunity to fight for the New York State Athletic Commission (NYSAC) World Bantamweight Title held by Charley Phil Rosenberg.

Graham boxed, feinted, and danced through the bout, but dealt a low blow to the "Kid" in the second that put him on the mat, and brought a warning from the referee.

After managing to stay on his feet, Graham hit a long left hook below the belt of Chocolate, which caused the referee to end the bout 2:04 into the seventh.

Graham had quite a late start, fighting on the defensive and losing on points until the last round, when in desperation he became the aggressor and knocked Miller to the canvas for a nine count with a left to the temple.

[3] On June 11, 1929, Graham had an important victory over Jewish boxer Archie Bell before a crowd of 4,000 in a ten-round decision at Artillery Park in Wilkes-Barre, Pennsylvania.

Within two months of the win and according to one source, shortly before it, Graham was recognized as the World Bantamweight Champion by the Pennsylvania Athletic Commission, though this was not a universal recognition.

[3][31] On August 26, 1929, Graham defeated Vidal Gregorio in a non-title match before a crowd of 7,500 in a ten-round points decision at the Arena in Philadelphia.

With arms dangling to the side, as was his custom, Graham delivered whistling rights to the chin and face of his opponent using speed rather than any advantage in reach to make his mark.

[32] On September 20, 1929, in the feature bout at Boston Garden, Graham lost to Andy Martin in a non-title ten round points decision.

[33][3] On May 28, 1930, Graham lost a ten-round points decision fought before a disappointing crowd of 5000, to former American and World Flyweight Champion Fidel LaBarba at New York's Madison Square Garden.

[3] Graham refused to mix with LaBarba, causing the bout to proceed slowly, and spark gentle protests from the small crowd present.

Before a mid-sized crowd of 3,500, he defeated Battalino, still NBA World Featherweight Champion, in Cincinnati's Redland Field in a ten-round non-title match on September 24, 1931.

The crowd found the bout dull, as few solid punches were landed, and a great deal of clinching occurred until the last three rounds when the boxers clashed more frequently.

[41][42] On April 8, 1932, Graham lost in a minor upset to Tommy Paul in a ten-round points decision at Olympia Stadium in Detroit, Michigan.

The opponents fought evenly for the first six rounds, but Paul pulled ahead in the seventh, planting a strong right on the cheek of Graham that opened an old cut.

The bout, which drew only a small crowd of 2,645, was the first of an elimination tournament sanctioned by the National Boxing Association to pick the new NBA World Featherweight Champion to succeed Bat Battalino, who had vacated the title.

[3] Graham, who was warned three times by the referee for avoiding and not actively engaging his opponent, danced and used his fancy footwork throughout the bout, but was booed my many for throwing far too few punches at Paul.

[46] On April 17, 1936, Graham won on a second-round technical knockout over Mexican American boxer Tony Herrera at the Arena in Syracuse, New York.

[47] Before a substantial late career crowd of 2,300, on June 15, 1936, Graham defeated Johnny Jadick, former Junior Welterweight Champion, in an eight-round points decision in Utica, New York.

[50] Shifting rapidly on defense and dancing to deliver pinpoint blows, Graham led in the early rounds, but tired as the bout continued.