Windjammer

Classical immunization assumes that you are immunizing against a single liability, and the yield curve makes a one-time parallel shift. This is an overly simplistic assumption since most liabilities aren't going to be bullet payments. Once you start to incorporate more realistic assumptions (i.e., multiple liabilities, non-parallel shifts, etc.), things get more complicated and you have to start thinking more about price risk and reinvestment risk.

A barbell strategy is going to have more interim coupon payments before your liability becomes due, thus you'll need to reinvest those coupons, meaning you have higher reinvestment risk.