For decarbonization purposes, variable renewable energies (VRE) are widely and quickly deployed in historically fossil-dominated power systems. Yet, some fossil technologies are more suitable than others for integration with VRE due to their higher flexibility. I utilize an analytically tractable model to study the optimal transition to a VRE-dominated sys-tem when the endowment of flexible and inflexible conventional generators is rigid. I find that the existence of inflexible fossil generators hampers early deployment of VRE. How-ever, deployment speed increases after VRE begin to substitute generation from inflexible generators, which happens after VRE and inflexible capacities strictly exceed demand together. At this time, the decreasing use of inflexible fossil generation is usually ac-companied by an increasing utilization of flexible generators. Nevertheless, constructing additional flexible capacities is only profitable under restrictive conditions. By contributing to a better understanding of the impact of flexibility on efficient VRE deployment, this work may facilitate an efficient transition process.