The objective of this work is to investigate whether joint optimization of short-term and long-term predictors manifests significant advantages over the sequential optimization in speech coding. We propose a new joint optimization method based on Wiener filtering. The proposed analysis model resolves the pitch-bias problem of classical LPC analysis by considering the contribution of the long-term predictor while optimizing the short-term predictor. Our approach to joint optimization is based on analysis-by-synthesis and guarantees the synthesis filter stability. By applying our proposed joint optimization approach to CELP coding we obtain superior objective and subjective performance relative to CELP coding with sequential optimization. To provide voice quality equivalent to that of sequentially optimized CELP, the jointly optimized coder needs fewer FCB pulses and requires a reduced bit budget for LPC quantization. Our listening tests suggest that the JCELP coder at 4.25 kbps is equivalent in quality to the G.729 at 8 kbps.