This paper discusses work relevant to small, low-cost, membrane-based lightweight adaptive fast steering mirrors. Small deformable membrane mirrors can in principle provide higher order modes such as defocus, coma, and astigmatism in addition to the frequently available tip and tilt modes. This work uses a small number of electrostatic actuators located very close to two opposite boundaries to avoid possible "print through" problems. A Green's function based formulation is used to obtain the analytical solution. The role of membrane tension on the available modes and stroke is examined in detail, and it is found that greater tension enables low-order correction modes, while small values of tension lead to higher order correction modes. Experimental work on an initial experimental model is also described.