In the RW, gems are often recut to increase their value.
A gemstone's value is partially determined by rarity, of course, but relative to others of its kind, it is based on the "4 C's"- Cut, Clarity, Carats, and Color.
For example, a rose cut diamond has a lot of mass (Carats), but may be increased in value by recutting to a brilliant cut if it is well done, despite losing a lot of its mass. Why? Because brilliant cuts have more visual appeal- the brilliant cut was designed to work better with diamond's refraction, so it has more fire and play of light. Its a prettier stone.
It may also increase in value if the material excised was of lesser quality. Cut off a couple of cloudy layers or excise some inclusions, and all of a sudden, the smaller stone looks much better than the larger original.
As for the methodology...Pyrex's suggestion seems sound to me.