I suppose the biggest caveat to this is that it requires projects with a 1+ week duration. A lot of our work is smaller, and as such can be completed in an hour or two. We'd be back to billing 0.10 of a week for 4 hours of work, for example.

I quite like the day/half-day workflow employed by many freelancers. I think that makes sense, and it also gives the designer greater freedom and flexibility to do "good" work.

Hourly billing is by it's nature quite restrictive, as you're aware that you want to ensure the client is only paying for the hours you're actually working. It's open to both over-servicing, and under quoting as it requires accuracy from all parties.

For most projects, I like to charge a daily rate. Most of my projects end up being between 1 and 1.5 weeks long. I also attach a schedule that summarizes what I plan to do and how many days of work each major task will take.

If the project ends up being more of a "day project", then I can can charge a full day or 0.5 day rate.

My clients seem to understand this format. I'd be interested to know if anyone else is doing something like this?

This is basically what SCRUM/Agile is like. Clients buy a chunk of development time and set priorities. Challenges with this approach with a fixed pricing model is that you're limiting the number of projects you can work on at the same time. Also I imagine that clients comparing vendors are confused by this approach. Agency A charges me $3000 for a website, while Agency B charges me $8000 for a week of work of 4 people. Next to that, Say a project goes fine on monday and tuesday but on wednesday 'shit' happens. You can't transfer to a different project until monday.

What works best is to basically set goals and a budget ceiling with your client in advance but don't limit yourself to a pre-defined timeframe or a single pricing model even within the scope of the project. Building something you've done plenty of times before like a WordPress site can be a fixed rate while the custom tailor made animation might be billed hourly.

Also give your clients an option to extend the scope of the project. Like, well after one iteration as agreed this is the design, which is o.k. but we feel it could be improved with a little more time and better photography which costs 'X'.

As someone else mentioned. Clients are usually not up front about their budgets. And most have no clue what anything costs. The quotes they receive might also vary from $300 to $10000 which isn't helping.

The (sometimes massive) discrepancy between how much work a project takes from a client's perspective and the actual amount of work required is one of the bigger challenges here, no?

I'd be interesting to see a meta-study or a retrospective on how different these are, on average.

Personally, I work in 2 week sprints. Client/Partner pays to budget the sprint and the rest of payment is given on delivery. If we like each other and things are going smooth, we continue on and draft up another 2 week sprint. This keeps us non-married in contract, and less risk for both parties. Has been working out well for me.