This paper introduces a new class of vector quantizers (VQs), called finite-state residual vector quantizers (FS-RVQs), and discusses their application to image compression. FS-RVQ may be viewed as a combination of residual vector quantization (RVQ) and finite-state VQ (FSVQ). It requires only a fraction of the codebook memory needed for conventional FSVQ and, in addition, has high computational efficiency. A design algorithm that jointly optimizes the RVQ stage codebooks with multipath searching and variable bit rate capability is introduced, and is used to design state codebooks. Simulation results show that FS-RVQ can perform better than VQ with only a fraction of the memory and complexity associated with FSVQ. For a fixed level of complexity, FS-RVQ can also outperform FSVQ.