One of the most important lessons from the success of deep learning is that learned representations tend to perform much better at any task compared to representations we design by hand. Yet evolution of evolvability algorithms, which aim to automatically learn good genetic representations, have received relatively little attention, perhaps because of the large amount of computational power they require. The recent method Evolvability ES allows direct selection for evolvability with little computation. However, it can only be used to solve problems where evolvability and task performance are aligned. We propose Quality Evolvability ES, a method that simultaneously optimizes for task performance and evolvability and without this restriction. Our proposed approach Quality Evolvability has similar motivation to Quality Diversity algorithms, but with some important differences. While Quality Diversity aims to find an archive of diverse and well-performing, but potentially genetically distant individuals, Quality Evolvability aims to find a single individual with a diverse and well-performing distribution of offspring. By doing so Quality Evolvability is forced to discover more evolvable representations. We demonstrate on robotic locomotion control tasks that Quality Evolvability ES, similarly to Quality Diversity methods, can learn faster than objective-based methods and can handle deceptive problems.