A study on finding new pulse shapes for binary CPM (Continuous Phase Modulation) signals to achieve better spectral and detection performance is carried out. Under the constraint that the power spectral density stays below the GSM spectral envelope, pulse shape is optimized to minimize the error probability. Polynomials are utilized in representing pulse shapes. The performance depends on the degree of the polynomials and the pulse length (L). With 8(th) degree polynomials having 4 free parameters, optimization is performed for the case L = 3. The performance of the CPM signal, having the pulse shape found by optimization, is compared with that of GMSK, currently being used as the GSM modulation scheme, and a gain of 1.1 dB is obtained with the optimum pulse shape (L = 3). Increasing pulse length, much better results are attained. With L = 7, the gain goes up to 2.3 dB with a considerable decrease in the sidelobes.