Estimation of model parameters is as important as model building, but is often neglected in model studies. Here we show that despite the existence of well known results on parameter estimation in a simple homogenous Ornstein-Uhlenbeck process, in most practical situations the methods suffer greatly from finite sample sizes and especially the estimator of the time constant of the system is degraded. Therefore an alternative solution is of paramount importance. We present such a solution based on perturbation of the system, observing trajectories far from equilibrium. The results are illustrated on computer experiments based on applications in neuroscience and pharmacokinetics, which show a striking improvement of the quality of estimation. The results are important for judicious designs of experiments to obtain maximal information from each data point, especially when samples are expensive or difficult to obtain.