In this paper we design bandwidth efficient parallel-concatenated Turbo Trellis Coded Modulation (TTCM) schemes for communicating over AWGN and uncorrelated Rayleigh fading channels. The convergence properties of the symbolbased TTCM schemes employing various constituent codes, were analysed using symbol-based EXtrinsic Information Transfer (EXIT) charts. The traditional method used of generating EXIT charts is based on computationally complex multidimensional histogram measurements, which is only feasible for analysing TTCM schemes employing loworder modulation schemes, such as 4PSK and 8PSK. Hence, a novel low-complexity technique was employed in this paper for computing the symbol-based EXIT charts. Capacity-approaching TTCM schemes were designed based on the best constituent codes found when employing 8PSK, 16QAM, 32QAM and 64QAM modulation schemes.