Most autosomal dominant (AD)-HSPs are pure, and SPG4, due to mutations in SPAST, is the most common genetic variant [1,2,3] Mutations in ATL1 (SPG3A), REEP1 (SPG31), and KIF5A (SPG10) are also relatively frequent; when combined with SPG4, these forms account for about 50–60% of AD-HSP families [8,9,10]. The gene discussed is REEP1; the disease is Alzheimer disease.