One of the standard principles of rationality guiding traditional accounts of belief change is the principle of minimal change: a reasoner's belief corpus should be modified in a minimal fashion when assimilating new information. This rationality principle has stood belief change in good stead. However, it does not deal properly with all belief change scenarios. We introduce a novel account of belief change motivated by one of Grice's maxims of conversational implicature: the reasoner's belief corpus is modified in a minimal fashion to assimilate exactly the new information. In this form of belief change, when the reasoner revises by new information (p OR q) their belief corpus is modified so that (p OR q) is believed but stronger propositions like (p AND q) are not, no matter what beliefs are in the reasoner's initial corpus. We term this conservative belief change since the revised belief corpus is a conservative extension of the original belief corpus given the new information.