Standard passive aerodynamic flow control devices such as vortex generators and gurney flaps have a working principle that is well understood. They increase the stall angle and the lift below stall and are mainly applied at the inboard part of wind turbine blades. However, the potential of applying a rigidly fixed leading-edge slat element at inboard blade stations is less well understood but has received some attention in the past decade. This solution may offer advantages not only under steady conditions but also under unsteady inflow conditions such as yaw. This article aims at further clarifying what an optimal two-element configuration with a thick main element would look like and what kind of performance characteristics can be expected from a purely aerodynamic point of view. To accomplish this an aerodynamic shape optimization procedure is used to derive optimal profile designs for different optimization boundary conditions including the optimization of both the slat and the main element. The performance of the optimized designs shows several positive characteristics compared to single-element airfoils, such as a high stall angle, high lift below stall, low roughness sensitivity, and higher aerodynamic efficiency. Furthermore, the results highlight the benefits of an integral design procedure, where both slat and main element are optimized, over an auxiliary one. Nevertheless, the designs also have two caveats, namely a steep drop in lift post-stall and high positive pitching moments.