This paper presents a new mechanism for a better exploitation of surrogate models in the framework of Evolution Strategies (ESs). This mechanism is instantiated here on the self-adaptive surrogate-assisted Covariance Matrix Adaptation Evolution Strategy (saACM-ES), a recently proposed surrogate-assisted variant of CMA-ES. As well as in the original saACM-ES, the expensive function is optimized by exploiting the surrogate model, whose hyper-parameters are also optimized online. The main novelty concerns a more intensive exploitation of the surrogate model by using much larger population sizes for its optimization. The new variant of saACM-ES significantly improves the original saACM-ES and further increases the speed-up compared to the CMA-ES, especially on unimodal functions (e.g., on 20-dimensional Rotated Ellipsoid, saACM-ES is 6 times faster than aCMA-ES and almost by one order of magnitude faster than CMA-ES). The empirical validation on the BBOB-2013 noiseless testbed demonstrates the efficiency and the robustness of the proposed mechanism.