In Australia, equal access share buybacks can be structured so that a portion of the buyback price is designated as a fully franked dividend. The tax benefits derived from this structure imply that off-market buybacks are sometimes offered to shareholders at a discount to the current market price. This is in contrast to the United States, which operates under a classical taxation system, and where off-market buybacks are generally executed at a premium to the market price. The situation in Australia provides a unique opportunity to add to our understanding of taxation explanations for how and why companies buy back their shares. We find that the size of the discount of the offer price to the current share price is significantly related to the proportion of the buyback price designated a franked dividend. Analysis of the after-tax benefits to shareholders leads us to conclude that the structure of many equal access buybacks in Australia is advantageous to superannuation funds holding the stock.