Let $\theta$ be a closed $(1,1)$-form whose de Rham class $\{\theta\}\in N^{1}(X)$ is ample. For every sufficiently high model $\mathcal{X}$, we may then find a model function $\varphi$ such that $\theta+dd^{c}\varphi$ is $\mathcal{X}$-positive. If $\theta$ is furthermore semipositive then we may also arrange that $-\varepsilon\leq\varphi\leq 0$ for any given $\varepsilon>0$.