The main goal of this project is to establish the o-minimality of an algebra containing multisummable functions and almost regular germs. An o-minimal structure is a framework for studying sets and functions with tame geometric behavior: in particular, every one-dimensional definable set is a finite union of points and intervals. This finiteness property leads to various uniform boundedness results and is a central source of tameness. Roughly speaking, the proof of o-minimality proceeds in two steps. The first is to construct a quasianalytic algebra of generalized variables. The second is to identify a suitable class of power series with coefficients in this algebra that remains stable under the operations needed in the construction. In this talk, I will describe the current progress of the project and explain the main ideas behind these two steps.