In mammals, X-inactivation establishes X-chromosome dosage parity between males and females. How X-chromosome counting regulates this process remains elusive, because neither the hypothesized inactivation "blocking factor" nor the required cis-elements have been defined. Here, a mouse knockout and transgenic analysis identified DNA sequences within the noncoding Tsix and Xite genes as numerators. Homozygous deficiency of Tsix resulted in "chaotic choice" and a variable number of inactive X's, whereas overdosage of Tsix/Xite inhibited X-inactivation. Thus, counting was affected by specific Tsix/Xite mutations, suggesting that counting is genetically separable from but molecularly coupled to choice. The mutations affect XX and XY cells differently, demonstrating that counting and choice are regulated not by one "blocking factor," but by both a "blocking" and a "competence" factor.