I will discuss the role of regularity properties in the structure and classification of C*-algebras, singling out the property of strict comparison of positive elements by traces. A well-understood source of strict comparison is through tensorial absorption of the Jiang-Su C*-algebra. This property is, however, absent from naturally occurring examples such as the reduced group C*-algebras of free groups. Thus, for some time this notion was hindered by a lack of concrete examples (particularly non-nuclear ones). This situation changed after the recent breakthrough work of Amrutam, Gao, Kunnawalkam Elayavalli, and Patchel. This work exploited the connection between Voiculescu's free independence and strict comparison, encapsulated in the concept of "selfless C*-algebra", to confirm that large classes of reduced group C*-algebras indeed obey strict comparison. I will discuss ongoing joint work with Hayes and Kunnawalkam Elayavalli, where we continue the program of verifying selflessness, and thus strict comparison, for new classes of C*-algebras, this time those arising as reduced free products.