There is a growing concern that the recent progress made in AI, especially regarding the predictive competence of deep learning models, will be undermined by a failure to properly explain their operation and outputs. In response to this disquiet counterfactual explanations have become massively popular in eXplainable AI (XAI) due to their proposed computational psychological, and legal benefits. In contrast however, semifactuals, which are a similar way humans commonly explain their reasoning, have surprisingly received no attention. Most counterfactual methods address tabular rather than image data, partly due to the nondiscrete nature of the latter making good counterfactuals difficult to define. Additionally generating plausible looking explanations which lie on the data manifold is another issue which hampers progress. This paper advances a novel method for generating plausible counterfactuals (and semifactuals) for black box CNN classifiers doing computer vision. The present method, called PlausIble Exceptionality-based Contrastive Explanations (PIECE), modifies all exceptional features in a test image to be normal from the perspective of the counterfactual class (hence concretely defining a counterfactual). Two controlled experiments compare this method to others in the literature, showing that PIECE not only generates the most plausible counterfactuals on several measures, but also the best semifactuals.