A new scheme of optical fibers with different types of end-faces by applying different types of periodical variable torques to control the polishing pressure is proposed and fabricated. Two types of mechanisms, mechanical torque and electrical torque controls, are developed to generate different types of periodical variable torques. The mechanical torque control type is mainly designed for fabricating an elliptical-cone-shaped fiber end-face that can be used in efficient coupling between a laser diode and fiber with a coupling efficiency up to 83% (Lu et al 2007 Opt. Express 15 1434). The electrical torque control type is even more versatile for fabricating optical fibers or micro-probes with polygon pyramid end-faces that may have other potential applications, such as various kinds of micro-indenters. Both types of fiber end-faces can deliver satisfactory results with single-step fabrication, a high fabrication yield and sufficient optical coupling efficiency.