Our starting point is the ascertainment that D-optimal input signals recently considered by the same authors [12] can be too dangerous for applying them to real life system identification. The reason is that they grow too fast in time. In order to obtain more safe input signals, but still leading to a good estimation accuracy of parameter estimates, we propose a quality criterion that is a mixture of D-optimality and a penalty for too fast growth of input signals in time.Our derivations are parallel to those in [12] up to a certain point only, since we obtain different optimality conditions in the form of an integral equation. We also briefly discuss a numerical algorithm for its solution.