We find a $C^{infty}$ one-parameter family of Riemannian metrics $g_t$ on $mathbb{R}^3$ for $0{leq}t{leq}{varepsilon}$ for some number ${varepsilon}$ with the following property: $g_0$ is the Euclidean metric on $mathbb{R}^3$, the scalar curvatures of $g_t$ are strictly decreasing in t in the open unit ball and $g_t$ is isometric to the Euclidean metric in the complement of the ball.