We investigate in this paper the properties of some dilatations or contractions of a sequence (αn)n≥1 of Lr-optimal quantizers of an ${ℝ}^d$-valued random vector $X\in L^r\left(\mathbb{P}\right)$ defined in the probability space $(\Omega ,𝒜,\mathbb{P})$ with distribution ${\mathbb{P}}_X=P$. To be precise, we investigate the Ls-quantization rate of sequences ${\alpha }_n^{\theta ,\mu }=\mu +\theta ({\alpha }_n-\mu )=\{\mu +\theta (a-\mu ),a\in {\alpha }_n\}$ when $\theta \in {ℝ}_{+}^{☆},\mu \in ℝ,s\in (0,r)$ or s ∈ (r, +∞) and $X\in L^s\left(\mathbb{P}\right)$. We show that for a wide family of distributions, one may always find parameters (θ,µ) such that (αnθ,µ)n≥1 is Ls-rate-optimal. For the Gaussian and the exponential distributions we show...