The paper presents new power and bandwidth efficient coding schemes that combine turbo codes with M-QAM modulation for fading channels. In the encoder, each group of information bits is associated with its parity check symbol which is alternately obtained from the first and second turbo component encoders. The coded digits of the two encoders are mapped to the in-phase and quadrature components of a modulation signal constellation separately. In the decoder, iterative decoding with symbol-by-symbol MAP algorithm can be employed. Using this approach, code schemes for bandwidth efficiencies of 2, 3 and 4 bits/s/Hz with M-QAM modulation are investigated. The simulation results show that the new schemes have superior performance to the known codes for the same bandwidth efficiency and interleaver size.