I will present an analysis of the sets that minimize the Gaussian perimeter plus the norm of the barycenter. These two terms are in competition, and in general the solutions are not the half-spaces. In fact we prove that when the volume is close to one, the solutions are the strips centered in the origin. As a corollary, we obtain that the symmetric strip is the solution of the Gaussian isoperimetric problem among symmetric sets when the volume is close to one. Co-Author: Vesa Julin