Free-space optical cross connect (OXC) for optical switching has shown promise in replacing traditional electronic switching fabrics. Micromachined optical switches offer superior performance in terms of bit rate and protocol transparency, which make them futureproof; however, they suffer from nonuniformity in port-to-port optical losses, which limit their use in large-scale optical connects. Recent reports on a novel two-dimensional (2-D) OXC architecture, L-switching matrix, presented that it can significantly improve nonuniformity in optical losses among all output ports. The drawback of L-switching matrix is that it is rearrangeably nonblocking (RNB) and not strictly nonblocking. This paper presents solutions to optimize its switching algorithms. A staircase-switching algorithm is proposed to minimize the occurrence of internal blocking conditions.