Let $\chi$ be a psh function on a subvariety $X\subset{\mathbb{C}}^{n}$ and let $v$ be a continuous psh function on ${\mathbb{C}}^{n}$ with $\chi<v$ on $X$. If $R>0$, there exists a psh function $\widetilde{\chi}=\widetilde{\chi}_{R}$ on ${\mathbb{C}}^{n}$ so that $\widetilde{\chi}\,|_{{}_{X}}=\chi$ and $\widetilde{\chi}(z)<v(z)$ for all $z\in{\mathbb{C}}^{n}$ with $\|z\|\leq R$.