The mantra says under-promise and over-deliver. But over-delivery lies in the eye of the customer and not in yours.
For example, if you say your estimated delivery day is Thursday, delivering on Wednesday is not great service if your customer comes home to find a failed delivery note.
You may well have gone the extra mile in respect of your normal performance. However, if it's not something that the customer appreciated then you weren't just wasting your time, you were potentially wasting theirs and that's unforgiveable.