Optical code-division multiple-access (OCDMA) is a promising technique for multimedia transmission in fiber-optic local-area networks (LANs). Variable-weight optical orthogonal codes (OOCs) can be used for OCDMA networks supporting multiple quality of services (QoS). Most constructions for optimal variable-weight OOCs have focused on the case where the number of distinct Hamming weights of all codewords is equal to two, and the codewords of weight 3 are normally included. In this letter, four explicit constructions of optimal (v,{4,5,6},1,Q)-OOCs are presented, and more new optimal (v,{4,5,6},1,Q)-OOCs are obtained via recursive constructions. These improve the existing results on optimal variable-weight OOCs with at least three distinct Hamming weights and minimum Hamming weight 4.