A valued field is called maximal if it admits no proper immediate extentions (having the same residue field and value group). Krull observed that every valued field must have some maximal immediate extension; Kaplansky established sufficient conditions for uniqueness. In doing so, Kaplansky proved that a field is maximal if and only if it is spherically complete: that the intersection of any chain of closed (valuative) balls is non-empty. As can be expected, spherical completeness can be convenient for analytic/geometric arguments. Model theoretically, it can be helpful to transfer to a spherically complete model, if at least one exists. But, while every valued field has a spherically complete extension, this need not be an elementary extension (even as a valued field). Furthermore, it might be important to preserve extra (algebraic/analytic) structure on the field. Cluckers, Halupczok and Rideau have recently introduced hensel minimality for expansions of valued fields. In this talk, we discuss the existence of spherically complete models of hensel minimal expansions of valued fields; joint work with Immanuel Halupczok.