The paper deals with an investigation that was carried out to determine whether simple data-compression techniques could be applied successfully to an experimental 9.6 kbit/s adaptive p.c.m. digital speech system: The main aim of the investigation was to ascertain whether compression factors of two or four could be achieved. In the paper, the results of the investigation are presented and it is shown that the adaptive p.c.m. system is converting speech into a 9.6 kbit/s digital form that appears to possess very little redundancy. The results of a statistical analysis of the data are given, and it is shown that a compression factor of two is unlikely to result in a speech quality that is commercially acceptable. The results of an experimental investigation that was carried out in support of the theoretical investigation are presented. The results of the experimental investigation show that although compression by a factor of two results in a speech quality that is commercially unacceptable, a 4/3 compression can be achieved without any serious degradation of the speech quality.