An asymmetric insulated-gate field effect transistor (100U or 102U) provided along an upper surface of a semiconductor body contains first and second source/drain zones (240 and 242 or 280 and 282) laterally separated by a channel zone (244 or 284) of the transistor's body material. A gate electrode (262 or 302) overlies a gate dielectric layer (260 or 300) above the channel zone. A pocket portion (250 or 290) of the body material more heavily doped than laterally adjacent material of the body material extends along largely only the first of the S/D zones and into the channel zone. The vertical dopant profile of the pocket portion is tailored to reach a plurality of local maxima (316-1-316-3) at respective locations (PH-1-PH-3) spaced apart from one another. The tailoring is typically implemented so that the vertical dopant profile of the pocket portion is relatively flat near the upper semiconductor surface. As a result, the transistor has reduced leakage current.