Here is how to solve the corners on a cube where it is possible to solve with half-twists only.

1. Solve the corners on one pair of opposite faces (if there is not already a solved pair) and place the cube so the solved faces are on the left & right.

2. If the misplaced facelets on the front face are horizontal then proceed to step three. If they are diagonal then half-twist the left or right face to make them horizontal. If they are vertical then half-twist the left and/or right face to solve the cube.

3. If the misplaced facelets on the front face are in the bottom row then solve as shown on the first cube below. If the misplaced facelets on the front face are in the top row then solve as shown on the second cube below.