Carbon taxation is a regressive policy which contributes to public opposition towards same. We employ the Exact Affine Stone Index demand system to examine the extent to which carbon taxation in Ireland reduces emissions, as well as its distributional impacts. The Engel curves for various commodity groupings are found to be non-linear, which renders the particular demand system we have chosen more suitable than other methods found in the extant literature. We find that a carbon tax increase can decrease emissions, but is indeed regressive. Recycling the revenues to households mitigates these regressive effects. A targeted allocation that directs the revenues towards less affluent households is found to reduce inequality more than flat allocation that divides the revenues equally amongst all households; however both methods are capable of mitigating the regressive effects of the tax increase.