Non-systematic (207, 187) Reed-Solomon codewords contain valuable information concerning the correctness of the outer convolutional coding of the serial concatenated convolutional coding (SCCC) used for transmitting digital television (DTV) data to mobile/handheld (M/H) receivers. M/H receivers are described that, before and during turbo decoding of the SCCC, decode (207, 187) Reed-Solomon (RS) coding of transport-stream packets encapsulating M/H DTV data. The results of the decoding the RS coding locate bytes in the outer convolutional coding of the SCCC very unlikely to be in error. The confidence levels of bits in those bytes are adjusted accordingly, so turbo decoding of the SCCC converges faster. In M/H receivers of preferred design, the results of decoding RS coded transport-stream packets are used to signal when such convergence is reached, to stop the iterative SCCC decoding procedures before a prescribed maximum number of iterations, thus to conserve operating power.