We present new rate distortion bounds for speech coding based upon new composite source models for speech and conditional rate distortion theory. The composite source models are constructed by classifying each sentence as Voiced (V), Unvoiced (UV), Onset (ON), Hangover (H), and Silence (S). A 10^th order AR model is used for the V mode, 4^th order AR models are used for the ON and H modes, and the UV mode is modeled as uncorrelated. Marginal rate distortion functions are computed for each mode and combined to produce conditional rate distortion bounds based on unweighted and weighted mean squared error distortion measures. For unweighted distortion measures, the new bounds imply that good performance is attainable at rates as low as 0.25 bits/sample for narrowband speech.