The present invention is a method for effecting rapid improvement in cognition in subjects suffering from conditions or diseases related to the A.beta. peptide, including Alzheimer's disease, Down's syndrome, cerebral amyloid angiopathy, mild cognitive impairment, and the like. The method comprises administering anti-A.beta. antibodies to the subject, especially antibodies having a high affinity for soluble forms of A.beta.. X-15240