Disclosed herein are various methods of forming spacers on FinFETs and other semiconductor devices. In one example, the method includes forming a plurality of spaced-apart trenches in a semiconducting substrate that defines a fin, forming a first layer of insulating material in the trenches that covers a lower portion of the fin but exposes an upper portion of the fin, and forming a second layer of insulating material on the exposed upper portion of the fin. The method further comprises selectively forming a dielectric material above an upper surface of the fin and in a bottom of the trench, depositing a layer of spacer material above a gate structure of the device and above the dielectric material above the fin and in the trench, and performing an etching process on the layer of spacer material to define sidewall spacers positioned adjacent the gate structure.