Polite alternatives to "as soon as possible"

An alternative I see in business emails is:

As soon as you get a chance.

I like it because it implies sensitivity for the other person's schedule yet conveys the urgency of the matter.

You could try at your earliest convenience, but there is a risk that somebody unfamiliar with idioms might take it as 'when convenient to yourself' (which is actually at your convenience).

Unlike what you feel, as soon as possible is not considered rude. The abbreviated asap is very common in business emails and is accompanied with a 'Please' to convey the sense of polite urgency.

Please finish this task asap.

One alternative to asap is at the earliest.

Please finish this task as soon as possible at the earliest.

Another choice would be to re-word your statement as follows.

I request you to expedite this task.

Expedite conveys the sense of urgency in a formal way.

I often need to ask for things to be returned to me. In a business setting, I have found that giving people a specific date (and sometimes a specific time) helps them. I always follow up with something like, "If you feel you need more time than that, please let me know." or "If this deadline is not feasible, please let me know." Adding that sentence shows the recipient that you are sensitive to his or her schedule. Giving a firm date helps the recipient be cognizant of your schedule.

I have found writing, "when you get a chance" or "as soon as possible" leaves it too much up in the air. And, as the saying goes, if it weren't for the last minute, nothing would ever get done. Your items of business will be pushed back in the recipient's schedule and then you find yourself trying to find a polite way to write, "where's my stuff!?!"