Cohort effects originate from environmental conditions, and can have long-term consequences for the cohort's performance. It has been proposed that cohort effects tend to increase population fluctuations. However, differences among individuals, which cohort effects introduce into a population, usually have stabilizing effects. There are thus two different predictions regarding the impact of cohort effects on population fluctuations. We argue that it is important to distinguish between environmental variability and its long-term effects on individual quality, and approach the question with a population model that can include or exclude such effects. We show that the influence of cohort effects depends on the inherent dynamics: cohort effects can have stabilizing effects if dynamics are inherently unstable. However, the most common outcome is destabilization whenever cohort effects act on top of inherently stable dynamics. Intriguingly, both alternatives are due to individual differences affecting the structure of density dependence in a similar way.