Fix $n\in\mathbb{N}$, $h_0>0$, and $m\in\mathbb{R}$. Let $a\in S^m_{1,0}(T^*\mathbb{R}^n)$ be uniformly semiclassical for $0<h\leq h_0$, and suppose that there are constants $c>0$ and $R>0$ such that

\begin{align*} |a(x,\xi;h)|\geq c\langle\xi\rangle^m \end{align*}

for every $x\in\mathbb{R}^n$, every $\xi\in\mathbb{R}^n$ with $|\xi|\geq R$, and every $0<h\leq h_0$. Let $A_h=\operatorname{Op}_h(a)$ be the left semiclassical quantization. Here $\Psi_h^{-\infty}(\mathbb{R}^n)$ denotes the ordinary uniformly smoothing semiclassical class: its full symbols lie in $S^{-N}_{1,0}(T^*\mathbb{R}^n)$ for every $N\in\mathbb{N}$, uniformly for $0<h\leq h_0$. No decay of order $O(h^N)$ for every $N$ is included in this notation. Then there is a symbol $b\in S^{-m}_{1,0}(T^*\mathbb{R}^n)$ such that, with $B_h=\operatorname{Op}_h(b)$, there exist $R_h,S_h\in\Psi_h^{-\infty}(\mathbb{R}^n)$ satisfying

\begin{align*} B_hA_h=I+R_h \end{align*}

and

\begin{align*} A_hB_h=I+S_h \end{align*}

as operators on $C_c^\infty(\mathbb{R}^n)$.