It's always a pleasant surprise when a package arrives a bit sooner than you expected. You get even more excited about the content you just received. It's also great when there is an extra gift in what you bought online. The same goes for business. We all love when a partner does the extra mile than what you planned. All these situations make people happy. That's why you should create such conditions from the start. For typical vendors, I would say: talk less, do more. If you know, you can deliver work in 2 days, then promise three days. If you do everything right, you create a day of happiness for you and the customer. If things go wrong, and you need a bit of extra time, then the customer won't notice it.
That can work for any service or product. The product promise should always be a bit smaller than the real outcome.