We are concerned with Kolmogorov complexity of strings produced by non-deterministic algorithms. For this, we consider binary recursively enumerable relations, named description modes. We give conditions on the class of description modes to provide a Kolmogorov entropy. Within this framework, we prove that there is a proper hierarchy of such non-deterministic modes. Then, we give a sharp estimation on the amount of information to turn a deterministic mode into a non-deterministic one, and inversely. Lastly, we show that deterministic modes are less efficient than non-deterministic modes from some rank.