In this paper new semilogarithmic quantizer for Laplacian distribution is presented. It is simpler than classic A-law semilogarithmic quantizer since it has unit gain around zero. Also, it gives for 2.97 dB higher signal-to-quantization noise-ratio (SQNR) for referent variance in relation to A-law, and therefore it is more suitable for adaptation. Forward adaptation of this quantizer is done on frame-by-frame basis. In this way G.712 standard is satisfied with 7 bits/sample, which is not possible with classic A-law. Inside each frame subframes are formed and lossless encoder is applied on subframes. In that way, double adaptation is done: adaptation on variance within frames and adaptation on amplitude within subframes. Joined design of quantizer and lossless encoder is done, which gives better performances. As a result, standard G.712 is satisfied with only 6.43 bits/sample. Experimental results, obtained by applying this model on speech signal, are presented. It is shown that experimental and theoretical results are matched very well (difference is less than 1.5%). Models presented in this paper can be applied for speech signal and any other signal with Laplacian distribution.