Even though Ivermectin was only shown to work against the COVID virus in vitro, and even though the FDA warned against its use in humans, many media outlets reported that research showed it was effective against COVID. The fact that they often did so without any caveats may have led readers to make unwarranted inferences and act on them, believing that their actions were supported by science. In order to mitigate against such outcomes, a 2017 paper that has been cited over 600 times so far urges authors to include Constraints on Generality (COG) statements. But do COG statements in fact work as intended? In the present experiment, participants were randomly assigned to read popular press articles with COG statements or those without, and answered a series of questions about the articles. We hypothesized that the inclusion of COG can (1) reduce the likelihood of prematurely making overly-confident and overly-generalized inferences after reading reports of research findings; (2) reduce the likelihood of acting on such inferences (e.g., ingesting untested substances); and (3) improve their understanding of science as a long-term, cumulative effort to reduce, but never eliminate, uncertainty. The data collected so far provide partial support for these hypotheses. We hope our findings will help the quality of popular press reporting of scientific findings, avoiding sensationalistic and over-confident content.