In this paper, we used the lossless compression algorithm of Hamming Correction Code Compressor (HCDC) in compressing the parameters of the ITU-T G.729 CODEC, which is the Conjugate Structure Algebraic Code Exited Linear Prediction. This standard has two rates; the standard rate with 8 Kbps and Annex D rate with 6.4 Kbps. The CODEC Parameters were generated using the standard ITU source Codes. These parameters includes linear prediction coefficients represented as LSPs, Gain and Excitation Bits, forming 80 bits for the standard rate and 64 bits for annex D rate. These bits are calculated over frames of 10 ms duration each. In this Papers; the HCDC compression algorithm was tested against both rates, the original signal's frames were grouped into four frames of 320 bits for 80 bits frames and 256 bits for annex D frames, then the compression performance were evaluated. Testing data set used were voices of four adult English speaking males and females. HCDC was able to reduce transmission rate by 50% in average for both CODEC rates. The results were compared to the entropy compression methods (Golomb-Rice) implemented in FLAC package, these methods could reduce the data rate by 22% in average. The overall compression performance were evaluated by averaging the compression rates for all frames for each sample in data set. HCDC were able to compress on parity=3 only. For other parity values; few blocks were valid, and the overall compression rate for frames were below 1.