Babbitt’s pre-compositional structures (partial orderings) serve as a series of game-like rules affecting the composition of surface details we hear. Especially in Babbitt’s late works (post-1980) these partial ordering rules vary drastically in terms of how much freedom they allow. This variance can be modeled mathematically (a computational formula is explained and visualized). This video (the second of a three-part video essay) reveals, in an excerpt from Babbitt’s 1987 sax and piano work _Whirled Series_, an intricate web of referential details (serial and tonal) that are improvised from the trillions of possibilities enabled by its background structure (partial ordering). The advantages of this peculiar improvisatory compositional situation in which Babbitt places himself are compared to visual art, chord-based bebop jazz improvisation, and to current ethics-infused philosophies of improvisation.