Code Excited Linear Prediction (CELP) algorithms are proposed for compression of speech in 8 kHz band at switched or variable bit rate and algorithmic delay not exceeding 2 msec. Two structures of Low-Delay CELP coders are analyzed: Low-delay sparse excitation and mixed excitation CELP. Sparse excitation is based on MP-MLQ and multilayer models. Mixed excitation CELP algorithm stems from the narrowband G.728 standard. As opposed to G.728 LD-CELP coder, mixed excitation codebook consists of pseudorandom vectors and sequences obtained with Long-Term Prediction (LTP). Variable rate coding consists in maximizing vector dimension while keeping the required speech quality. Good speech quality (MOS=3.9 according to PESQ algorithm) is obtained at average bit rate 33.5 kbit/sec.