The relay-feedback test is a simple and widely used identification tool for obtaining dynamic information that is useful for tuning feedback controllers. The height of the change in the manipulated variable h is specified, the test is run, and two parameters are normally obtained: the amplitude of the periodic output curve alpha (from which the ultimate gain K-u can be calculated) and the ultimate period P-u. These two parameters provide important information, but they are not sufficient for determining controller tuning for some processes; the most important being processes with large deadtimes. Many authors have suggested methods for extending this type of test in order to obtain additional information: run an additional step test, run a second relay-feedback test with a known dynamic element inserted in the loop, etc. This paper discusses the idea of avoiding these additional tests by simply looking at the shape of the output curve. First-order processes with small deadtime-to-time constant ratios (D/tau) give output curves that are triangular in shape. Large ratios yield curves that are a series of rectangular pulses. A simple characterization factor is proposed for quantifying the curve shape. This additional shape information can be used to determine all three parameters of a first-order/deadtime process (gain, deadtime, and time constant) from one relay-feedback test.