A method of forming a recessed access device comprises forming a trench in semiconductor material. Sidewalls and a bottom of the trench are lined with low-k gate-insulator material. The low-k gate-insulator material is characterized by its dielectric constant k being no greater than 4.0. Sacrificial material is formed in a bottom portion of the trench over the low-k gate-insulator material and over the trench bottom. A high-k gate-insulator material is formed in an upper portion of the trench above the sacrificial material and laterally-inward of the low-k gate-insulator material that is in the upper portion of the trench. The high-k gate-insulator material is characterized by its dielectric constant k being greater than 4.0. The sacrificial material is replaced with a conductive gate that has its top above a bottom of the high-k gate-insulator material. A pair of source/drain regions is formed in upper portions of the semiconductor material on opposing lateral sides of the trench. A channel region is in the semiconductor material below the pair of source/drain regions and extends along the trench sidewalls and around the trench bottom. Other embodiments, including structure independent of method, are disclosed.