In this paper, we address the problem of optimal bit allocation for stereo images. Conventional rate-distortion based methods have mainly concentrated on minimizing total distortion within a given bit budget by independently encoding each image. However, stereo image coding, like video coding, requires dependent bit allocation framework to further improve encoding performance because binocular and spatial dependencies are introduced by the disparity estimation and differential pulse coded modulation of the disparity vector field. We first formulate the dependent bit allocation problem for stereo image coding and extend it to blockwise dependent bit allocation. We then focus on the blockwise dependent quantization because using open-loop disparity estimation decouples the dependent bit allocation problem into two independent problems; disparity estimation and dependent quantization. The encoding complexity and delay in the dependent quantization framework can be significantly reduced by exploiting the unidirectional binocular dependency. An optimal set of quantizers can be selected using the Viterbi algorithm. For a given three quantization scales, the proposed scheme provides higher PSNR, about 3dB compared to JPEG without disparity compensation and 0.5dB compared to optimal higher PSNR, about 3dB compared to JPEG without disparity compensation and 0.5dB compared to optimal independent blockwise quantization with disparity compensation and 0.5dB compared to optimal independent blockwise quantization with disparity compensation. The proposed scheme can help develop a fast and efficient bit allocation strategy, be a benchmark of practical rate control schemes or be used in asymmetric applications, which may involve offline encoding, such as CD-ROM, DVD, video-on-demand, etc.