International Telemetering Conference Proceedings / October 20-23, 2003 / Riviera Hotel and Convention Center, Las Vegas, Nevada / Shaped Offset Quadrature Phase Shift Keying (SOQPSK) has the advantages of low sidelobes and high detection probability; however, its main lobe has a fixed width set by the number of constellation points. By slightly modifying the modulation scheme, the four constellation points of quadrature shift keying can be changed to M constellation points where M is a power of 2. After this change, the power spectral density (PSD) retains low sidelobes, and the desirable property of being able to detect the signal by integrating over two symbol periods is retained.