In this paper we present our work on improving the efficiency of adversarial training for unsupervised video summarization. Our starting point is the SUM-GAN model, which creates a representative summary based on the intuition that such a summary should make it possible to reconstruct a video that is indistinguishable from the original one. We build on a publicly available implementation of a variation of this model, that includes a linear compression layer to reduce the number of learned parameters and applies an incremental approach for training the different components of the architecture. After assessing the impact of these changes to the model's performance, we propose a stepwise, label-based learning process to improve the training efficiency of the adversarial part of the model. Before evaluating our model's efficiency, we perform a thorough study with respect to the used evaluation protocols and we examine the possible performance on two benchmarking datasets, namely SumMe and TVSum. Experimental evaluations and comparisons with the state of the art highlight the competitiveness of the proposed method. An ablation study indicates the benefit of each applied change on the model's performance, and points out the advantageous role of the introduced stepwise, label-based training strategy on the learning efficiency of the adversarial part of the architecture.