Sixteen-bit, programmable, digital-signal processors suffer from inadequate dynamic range and noise performance due in part to the use of standard data formats with few bits available for numeric precision. A solution to this problem is developed that involves the use of irregular data formats. A new class of irregular floating-point formats is developed. A specific format is derived from this class that provides greater dynamic range and improved noise performance for 16-bit DSP applications. An experiment with one of the new formats is conducted and analyzed, and improved performance is verified. The importance of our work and its potential applications are discussed.