In general, low rate speech coding systems do not have their own mechanism to reduce background noise from the speech signal. This is due to the complexity of the speech signal and limitations in the scope of many speech coding systems. As a consequence, most speech enhancement systems to date have attempted to process the speech waveform directly and independently from the speech coding system, before the encoding of the speech signals. In this paper, we propose several methods to optimize speech enhancement techniques in order to improve the estimation of the CELP speech codec parameters (short-term and long-term parameters). Experimental results for two speech enhancement techniques are presented in conjunction with the ETSI AMR speech codec.