Innovations in phase quantization during speech encoding and phase reconstruction during speech decoding are described. For example, to encode a set of phase values, a speech encoder omits higher-frequency phase values and/or represents at least some of the phase values as a weighted sum of basis functions. Or, as another example, to decode a set of phase values, a speech decoder reconstructs at least some of the phase values using a weighted sum of basis functions and/or reconstructs lower-frequency phase values then uses at least some of the lower-frequency phase values to synthesize higher-frequency phase values. In many cases, the innovations improve the performance of a speech codec in low bitrate scenarios, even when encoded data is delivered over a network that suffers from insufficient bandwidth or transmission quality problems.