While the crucial property of a dynamical system is its asymptotic stability, less is known about transient processes (behavior of the system at finite time instants). Even in linear systems, both continuous and discrete time, intermediate values of the variables can largely deviate (e.g., overshoot) from the reference signal. We can also observe undesirable "peaks" during time evolution of the system outputs, even if the system poles are chosen in a "good" fashion. Usually, such behavior is described in terms of step-response, assuming zero initial conditions. We'll show that nonzero initial conditions also play an important role in transient processes and should be taken into account. Clearly, such phenomena should be avoided in applications such as calibration of medical devices, exact targeting, control, dynamical estimation, etc. we show how to evaluate deviations caused by nonzero initial conditions and how to possibly smoothen this effect in the design.