Tuning of feedback controllers for SISO systems often starts from information about the intersection of the Nyquist curve and the negative real axis. In standard autotuning this point is identified by a relay feedback experiment. For many processes, however, it would be advantageous to identify a point on the Nyquist curve somewhere in the third quadrant. The aim of this paper is two-fold. First, a noniterative procedure is suggested for identification of an arbitrarily chosen point in the third quadrant by the use of a two-channel relay. The two-channel relay consists of two relays operating in parallel on the process output and on the integral of the process output, respectively. Secondly, general a priori plant knowledge, often available, is utilized for the choice between PI and PID control and for amplitude-and-phase-margin based controller tuning.