The paper describes five detection processes that are significant improvements of some recent developments of the Viterbi-algorithm detector. The new processes do not involve either excessive storage or an excessive number of operations per received signal-element, and do not require the use of an adaptive linear filter ahead of the detector, being therefore well suited to applications of digital data transmission over practical voice-frequency channels. Results of computer-simulation tests are presented comparing the tolerances to additive Gaussian noise of the new detection processes with those of the original processes, for many different channels