I would probably have to go with Monk in the second spot, but then again, Billy Strayhorn doesn't really get his due for his contributions to the Ellington band. Strayhorn and Duke were just a perfect team. The Far East Suite is still one of my all-time favorite jazz albums. Oliver Nelson is another guy who doesn't get his deserved recognition as a composer, IMO. As an arranger Nelson was second to none. Charles Mingus was a master composer, and Charlie Parker and Dizzy Gillespie both composed their share of tunes that are now jazz standards. Hoagy Carmichael wrote a lot of great early jazz tunes, but also wrote a lot of pop classics as well. Tito Puente composed a good number of classics in the Latin jazz genre (Oye Como Va, Ran Kan Kan, Picadillo, Para Los Ruberos, etc.). Fats Waller was another great composer that unfortunately doesn't get the recognition he deserves, but some of that has to do with the fact that he had a bad drinking habit and was not good with his money, which resulted in him selling the rights to a lot of his compositions, which others then put their own names on. Herbie Hancock certainly has his fair share of excellent compositions as well.