This paper argues that the crossword puzzle analogy is great for scientific rationality, but not scientific warrant. It provides a critical analysis of foundherentist conceptions of scientific warrant, especially that of Susan Haack, and closely related positions, such as non-doxastic coherentism. Foundherentism takes the middle ground between foundationalism and coherentism. The main idea is that warrant, including that of scientific theories, is like warrant of crossword entries: the degree to which a theory is warranted depends on one’s observations, the extent to which it coheres with one’s other scientific theories and whether one’s evidence includes a sufficiently large portion of the relevant evidence. I identify three problems for a foundherentist conception of scientific warrant, two of which are also problems for the image of science as a crossword puzzle. First, Haack’s conceptions of personal and social warrant of scientific theories are incompatible. Second, the notion of warrant defeaters is crucial to any account of warrant, but foundherentism cannot accommodate certain warrant defeaters. Third, Haack’s treatment of inconsistent evidence renders her account of social warrant for scientific theories implausible. Finally, I suggest that switching from the objective notion of warrant to the subjective notion of rationality might save foundherentism about scientific theories and the image of science as a crossword puzzle. I also draw lessons for social epistemology generally by applying the distinction between warrant and rationality to non-doxastic coherentism and Paul Faulkner’s hybrid theory of testimonial warrant.