Whether provided by a composer, written out by a performer or completely improvised, the cadenza became a vehicle for performers' creativity, lyricism and technical prowess in the eighteenth and nineteenth centuries. The debate about whether to notate or improvise cadenzas, a question as old as the cadenza itself, continues today. Saxophonists have not been involved in this debate, since the instrument is a product of the mid-nineteenth century and was in its infancy just as the practice of improvising cadenzas was fading. This study documents an unprecedented, recently-recorded, improvised cadenza in one of the most significant twentieth-century saxophone works: Jacques Ibert's Concertino da Camera for Alto Saxophone and Eleven Instruments (1935). Saxophonist Branford Marsalis's neo-cadenza for Ibert's composition presents an aggregate of the twenty-first-century performer improvising a cadenza to a twentieth-century work, in a tradition that was common centuries ago. The document begins with an inquiry into improvised cadenzas, and proceeds to an examination of the performance history of the cadenza for the Concertino da Camera. Twenty professionally-recorded versions of the cadenza are presented in order to understand the performance history of the cadenza, and to place the Marsalis cadenza into context. This research culminates in a transcription and analysis of the cadenza as improvised and recorded by Marsalis. Remarks from a personal interview with Marsalis are also included.