In this paper we present a novel defogging technique, named CurL-Defog, aimed at minimizing the creation of artifacts. The majority of learning based defogging approaches relies on paired data (i.e., the same images with and without fog), where fog is artificially added to clear images: this often provides good results on mildly fogged images but does not generalize well to real difficult cases. On the other hand, the models trained with real unpaired data (e.g. CycleGAN) can provide visually impressive results but often produce unwanted artifacts. In this paper we propose a curriculum learning strategy coupled with an enhanced CycleGAN model in order to reduce the number of produced artifacts, while maintaining state-of-the- art performance in terms of contrast enhancement and image reconstruction. We also introduce a new metric, called HArD (Hazy Artifact Detector) to numerically quantify the amount of artifacts in the defogged images, thus avoiding the tedious and subjective manual inspection of the results. The proposed approach compares favorably with state-of-the-art techniques on both real and synthetic datasets.