Although a FWW saying the WORDS "I'm sorry" are important (although for some betrayed husbands, it's a dealbreaker and I respect that) . . . I think an overall ATTITUDE of remorse is imperative.
I don't think I've ever seen a successful reconciliation where the formerly cheating spouse didn't convey that attitude, and where they didn't do the lion's share of the heavy relationship repair in the early "piecing" stage (at least after the "hard withdrawal" period of the first couple of weeks passes).
