One of the problems many people encounter when moving to agile is that they (literally) cannot imagine iterations shorter than 4 weeks.
I rarely recommend an iteration as long as 4 weeks now, and if people insist on 3 weeks, suggest they find the root cause for the reason their iteration needs to be so long. “Our builds take too long” or “our testing takes too long” are the most common problems I've heard. If you know what causes you to need more time, you can make a conscious decision about what to do. Do you want to address that technical debt now? or later? Every time your iteration needs to be long, it's because you have technical debt of some sort. You can choose not to address that debt now–but be conscious of that debt.
There was a question about the length of iterations on the scrumdevelopment list. Ron Jeffries said that he and Chet regularly paired in 2-hour iterations. With our teleclass, Gil and I often pair for an hour or two. We decide in advance how long to pair for, so we timebox our time, and then we do the work.. We have daily standups where we replan what we're doing for the day.
Does it make sense for you to have one-day or shorter iterations? It depends on who your customer is and when you can get feedback. But why not consider how short your iterations could be, and remove the obstacles to those shorter iterations? Your project will thank you.