Conjunctive causes are causes that all need to be present for an effect to occur. They contrast with independent causes that by themselves can each bring about an effect. We extend existing causal power representations of independent causes to in-clude a representation of conjunctive causes. We then demon-strate how independent vs. conjunctive representations imply sharply different patterns of reasoning (e.g., explaining away effects for independent causes as compared to exoneration ef-fects for conjunctive causes). An experiment testing how peo-ple reason with independent and conjunctive causes found that their inferences generally matched the models prediction, al-beit with some important exceptions.