This paper is concerned with the utilization of speech waveform periodicities in differential pulse code modulation (dpcm) coding with 2‐bit adaptive quantization and time‐invariant spectrum prediction. Our work is based on computer simulations of dpcm codes. We have studied pitch detectors based on autocorrelation and an average magnitude difference function (amdf), and we have measured the benefits of predicting from a previous pitch period as functions of pitch‐period‐updating frequency and periodicity‐indicating thresholds (for autocorrelation and the amdf). We have compared several alternative methods of utilizing past quantized samples (in the present and previous pitch periods) for providing speech sample predictions. We find the following combination to be attractive for waveform coding at bit rates in the neighborhood of 16 kb/s: 2‐bit adaptive quantization with a one‐word (2‐bit dpcm word) memory, pitch detection performed on unquantized speech (preferably with an amdf criterion) and a prediction scheme that uses fixed three‐tap (short‐term) prediction for nonperiodic waveform segments, but switches to an appropriate one‐tap (long‐term) predictor upon the detection of strong periodicity. With four sample utterances, the latter procedure results in an average SNR (signal‐to‐noise ratio) gain of 3.75 dB over a non‐pitch‐adaptive encoder.