Quality-Diversity optimisation algorithms enable the evolutionof collections of both high-performing and diverse solutions.These collections offer the possibility to quickly adapt andswitch from one solution to another in case it is not workingas expected. It therefore finds many applications in real-worlddomain problems such as robotic control. However, QD algo-rithms, like most optimisation algorithms, are very sensitive touncertainty on the fitness function, but also on the behaviouraldescriptors. Yet, such uncertainties are frequent in real-worldapplications. Few works have explored this issue in the spe-cific case of QD algorithms, and inspired by the literature inEvolutionary Computation, mainly focus on using samplingto approximate the ”true” value of the performances of a solu-tion. However, sampling approaches require a high number ofevaluations, which in many applications such as robotics, canquickly become impractical.In this work, we propose Deep-Grid MAP-Elites, a variantof the MAP-Elites algorithm that uses an archive of similarpreviously encountered solutions to approximate the perfor-mance of a solution. We compare our approach to previouslyexplored ones on three noisy tasks: a standard optimisationtask, the control of a redundant arm and a simulated Hexapodrobot. The experimental results show that this simple approachis significantly more resilient to noise on the behavioural de-scriptors, while achieving competitive performances in termsof fitness optimisation, and being more sample-efficient thanother existing approaches.