One property that remains lacking in image captions generated by contemporary methods is discriminability: being able to tell two images apart given the caption for one of them. We propose a way to improve this aspect of caption generation. By incorporating into the captioning training objective a loss component directly related to ability (by a machine) to disambiguate image/caption matches, we obtain systems that produce much more discriminative caption, according to human evaluation. Remarkably, our approach leads to improvement in other aspects of generated captions, reflected by a battery of standard scores such as BLEU, SPICE etc. Our approach is modular and can be applied to a variety of model/loss combinations commonly proposed for image captioning.