The paper studies some novel techniques for simplifying a near-maximum-likelihood detector that operates on a sequence of received samples, each of which carries two new data symbols. The two data symbols may originate from independent sources, and one of these may be an unwanted interfering symbol. In a received sample, the two new data symbols have been multiplied by arbitrary quantities that may vary independently, but smoothly, from one sample to the next. The new techniques are studied for a particular application of near-maximum-likelihood detection in a land-mobile-radio system, which introduces flat fading into the transmitted QPSK data signals. The receiver here employs an arrangement of combined detection and estimation that has recently been developed for use with the given signals. The arrangement enables two QPSK signals to be transmitted simultaneously over any one channel, in place of the one QPSK signal conventionally used, leading to a more efficient use of bandwidth. The paper shows how substantial simplifications may be introduced into the detection process without, however, significantly changing its resultant operation. The new techniques described here are of quite general application to many near-maximum-likelihood detectors, in applications over flat fading or frequency-selective fading channels, or over time invariant channels that introduce intersymbol interference.