The Church Frowns Mightily on the "Snip".
Listen - you can already hear the shouts "The Church has no business dictating our reproductive lives." Yeah...whatever.
The General Handbook is not definitive, but it is direct: "The Church strongly discourages surgical sterilization as an elective form of birth control. Surgical sterilization should be considered only if (1) medical conditions seriously jeopardize life or health or (2) birth defects or serious trauma have rendered a person mentally incompetent and not responsible for his or her actions. Such conditions must be determined by competent medical judgment and in accordance with law. Even then, the persons responsible for this decision should consult with each other and with their bishop and should receive divine confirmation of their decision through prayer."
Basically, the decision is an important one, and the Holy Ghost had better sign off on it first.
Of course the argument could be made that the fear of your wife having to eternally wear size 16 jeans falls under the category of "seriously jeopardizing life or health."
Also: There is a great blog which courageously addresses this subject. Read the comments too.