Restrictions on transaction price changes are a feature of many security markets. This paper analyzes the impact of such price continuity rules on price dynamics and examines possible rationales for their existence. Contrary to popular belief, continuity rules need not reduce price efficiency, although they do result in a redistribution of profits among traders and dealers. Indeed, continuity rules may enhance price efficiency because traders have greater incentives to gather costly information. We provide a new rationale for continuity rules besides the stated objective of stabilizing prices. In particular, we show that continuity requirements act to restrict dealers' expected profits from trading with liquidity traders. The results provide insights into the design of an “optimal” continuity rule.