Feelings of invulnerability, seen in judgments of 0% risk, can reflect misunderstandings of risk and risk behaviors, suggesting increased need for risk communication. However, judgments of 0% risk may be given by individuals who feel invulnerable, and by individuals who are rounding from small non-zero probabilities. We examined the effect of allowing participants to give more precise responses in the 0-1% range on the validity of reported probability judgments. Participants assessed probabilities for getting H1N1 influenza and dying from it conditional on infection, using a 0-100% visual linear scale. Those responding in the 0-1% range received a follow-up question with more options in that range. This two-step procedure reduced the use of 0% and increased the resolution of responses in the 0-1% range. Moreover, revised probability responses improved predictions of attitudes and self-reported behaviors. Hence, our two-step procedure allows for more precise and more valid measurement of perceived invulnerability. [Authors]