Mechanical properties of fiber-reinforced laminated composite materials are directionally dependent. Contemporary laminated composite design aims to make effective use of these directional properties by means of stacking sequence design, selecting the fiber orientation angle of each ply from a predefined set. Automated fiber-placement (AFP) technology can be used to improve the efficacy of composite materials by means of fiber steering. The variation of fiber orientation angles per ply of the laminate yields a variable stiffness (VS) laminate. For optimization purposes it is attractive to design such laminates in terms of lamination parameters (LP), as the number of design variables per point in the structure can be reduced to as little as four dimensionless variables considering balanced symmetric layups, and because many lay-up optimization problems can be made convex by describing them in terms of LPs. VS laminate design in terms of LP requires the obtained LP distribution to be converted into an actual fiber angle design. In a previous study the authors proposed a method to convert VS laminate designs using LPs into fiber angle designs. This method includes a constraint on in-plane curvature, a manufacturing constraint related to AFP. Thickness build-up will occur due to fiber steering. The amount of thickness build-up that results from the obtained fiber angle designs is discussed here as a function of the constraint on fiber curvature. The streamline analogy is used to obtain an estimate for thickness build-up and to determine fiber paths. A square plate loaded in biaxial compression is used to demonstrate the effect of the in-plane curvature constraint on thickness build-up, and several fiber angle designs, thickness distributions and fiber paths are given for this structure.