More than 100 loci have been identified for age at menarche by genome-wide association studies; however, collectively these explain only ∼3% of the trait variance. Here we test two overlooked sources of variation in 192,974 European ancestry women: low-frequency protein-coding variants and X-chromosome variants. Five missense/nonsense variants (in ALMS1/LAMB2/TNRC6A/TACR3/PRKAG1) are associated with age at menarche (minor allele frequencies 0.08-4.6%; effect sizes 0.08-1.25 years per allele; P<5 × 10(-8)). In addition, we identify common X-chromosome loci at IGSF1 (rs762080, P=9.4 × 10(-13)) and FAAH2 (rs5914101, P=4.9 × 10(-10)). Highlighted genes implicate cellular energy homeostasis, post-transcriptional gene silencing and fatty-acid amide signalling. A frequently reported mutation in TACR3 for idiopathic hypogonatrophic hypogonadism (p.W275X) is associated with 1.25-year-later menarche (P=2.8 × 10(-11)), illustrating the utility of population studies to estimate the penetrance of reportedly pathogenic mutations. Collectively, these novel variants explain ∼0.5% variance, indicating that these overlooked sources of variation do not substantially explain the 'missing heritability' of this complex trait.