Fixed-mirror solar concentrators (FMSCs) use a static reflector and a moving receiver. They are easily installable on building roofs. However, for high-concentration factors, several flat mirrors would be needed. If curved mirrors are used instead, high-concentration levels can be achieved, and such a solar concentrator is called a curved-slats fixed-mirror solar concentrator (CSFMSC), on which little information is available. Herein, a methodology is proposed to characterize the CSFMSC using 3D ray-tracing tools. The CSFMSC shows better optical characteristics than the FMSC, as it needs fewer reflector segments for achieving the same concentration and optical efficiency.