This paper addresses the problem of very-low-rate compression of digitized wideband speech signals for storage. It concentrates on applications where the text transcription of the speech corpus is available and where high quality of recovered speech is required. Following the problem statement, all unique features of the task are analysed and possible methods of implementation discussed. As a result, a novel speech compression technique is proposed, its general structure is presented, and its characteristics are considered. The new compression technique - hybrid speech compression - takes full advantage of the available text transcription. The proposed hybrid compression approach utilises an optimum balance of Text To Speech (TTS) synthesis technology with dynamic speech conversion to yield a data stream comprising original text enriched by prosodic features and conversion control information. The proposed speech compression method aims to achieve an extremely low data rate while preserving a high quality of the compressed wideband speech.