Covenant Marriages are marriages between a man and woman; the difference from traditional marriage is that they add some line items to the contract where they agree to obtain pre-marital counseling and accept more limited grounds for divorce. This could be a better recipe for successful marriages. Both parties have already agreed to limited terms of the contract, other than just love, honor and obey. It appears that these marriages may lead to more mature relationships, that could lead to a reduction of domestic violence cases.
Spousal abuse has shown us time after time that is cannot be so easily dismissed with a little counseling and lecturing. Abusers generally have turned manipulation and oppression into an art form. Covenant marriages would be a perfect tool for abusers as it gives them one more thing to hold over their spouses head to keep them trapped in a regrettable partnership at best, and potentially fatal one at worst.