Despite the clamor to speed up the U.S. vaccination drive against COVID-19, the first three months of the rollout suggest faster is not necessarily better. A surprising new analysis found that states such as South Carolina, Florida and Missouri that raced to offer the vaccine to ever-larger groups of people have vaccinated smaller shares of their population than those that moved more slowly and methodically, such as Hawaii and Connecticut. The explanation, as experts see it: The rapid expansion of eligibility caused a surge in demand too big for some states to handle. The result was serious disarray, confusion and frustration. The analysis may hold an important lesson for states as they rush to meet President Joe Biden’s goal of making all adults eligible for vaccination by May 1.