It is widely reported in the literature that incremental clustering systems suffer from instance ordering effects and that under some orderings extremely poor clusterings may be obtained. In this paper we present a new general strategy aimed to mitigate these efects, the Not-Yet strategy, which has a general and open formulation and it is not coupled to any particular system. In addition, we propose a classification of strategies to avoid ordering effects which clarifies the benefits and disadvantages we can expect from the proposal made in the paper as well from existing ones. A particular implementation of the Not-Yet strategy is used to conduct several experiments. Results suggest that the strategy can improve the clustering quality and also that performance is limited by its local nature. We also show that, when combined with other local strategies, the Not-Yet strategy may help the system to get high quality clusterings. The observed benefits and limitations suggest future work under the proposed framework.