  Rapha\"{e}l Rouquier introduced an invariant of triangulated categories which
is known as Rouquier dimension. Orlov conjectured that for any smooth
quasi-projective variety $X$ the Rouquier dimension of $D^b_{\mathrm{coh}}(X)$
is equal to $\mathrm{dim}\, X$. In this note we show that some blow-ups of
projective spaces satisfy Orlov's conjecture. This includes a blow-up of
$\mathbb{P}^2$ in nine arbitrary distinct points, or a blow-up of three
distinct points lying on an exceptional divisor of a blow-up of $\mathbb{P}^3$
in a line. In particular, our method gives an alternative proof of Orlov's
conjecture for del Pezzo surfaces, first established by Ballard and Favero.
