Let $\mathcal F$ be a pointwise measurable class of real-valued functions. Conditional on $X_1,\dots,X_n$, let $(Z_f)_{f\in\mathcal F}$ be the centred Gaussian process \begin{align*} Z_f=\frac{1}{\sqrt n}\sum_{i=1}^{n}g_i f(X_i), \end{align*} where $g_1,\dots,g_n$ are i.i.d. standard Gaussian random variables independent of the sample. Then \begin{align*} \mathbb E_\varepsilon\left[\sup_{f\in\mathcal F}R_n(f)\right] \le \sqrt{\frac{\pi}{2}}\,\mathbb E_g\left[\sup_{f\in\mathcal F}Z_f\right], \end{align*} whenever the displayed conditional expectations are finite. Moreover the canonical semimetric of $(Z_f)_{f\in\mathcal F}$ is $d_n$.