In the Viterbi-algorithm detection of a multilevel digital signal having a large alphabet (many levels), such as a 16-level QAM signal, very considerable equipment complexity is involved, even when the sampled impulse response of the channel has only a few components. A recent development of the Viterbi-algorithm detector, known as the pseudobinary Viterbi-algorithm detector, effectively recodes the received multilevel data signal into a binary signal and implements the conventional Viterbi-algorithm detection process for the corresponding binary signal, thus very greatly reducing the complexity of the detector. Since there is only a small loss in tolerance to noise as a result of the given modification, a potentially useful detection process is obtained. The paper describes two novel detection processes in which the given pseudobinary technique is applied to two different near-maximum-likelihood detectors. The particular application studied is that of a synchronous serial 9600 bit/s modem transmitting a 16-level QAM signal over a telephone circuit in the public switched telephone network. Results of computer simulation tests are presented, comparing the tolerances to additive white Gaussian noise of various arrangements of each detector, when operating over models of two different telephone circuits.