I'm probably late with comments, but here they go anyways.
First of all, I am an ideal target user of the service. I know my way around applied cryptography, I can appreciate properly designed system, and I am really protective of the privacy of my data when it leaves my immediate vicinity. Properly encrypted backups is my kind of thing.
Your existing website is not minimalistic. The lack of the design is not a minimalism, it's a manifestation of the visual presentation of the product not being a priority.
The site looks like a personal webpage from the early 90s, implying lots of things but none for those that I would want to see in the backup service provider. I have visited tarsnap website on multiple occasions before; primarily through the references on the cryptography maillist. And I have always assumed it was either a hobby or an academic project.
Since you have had the site redesigned, I am assuming that you realized the impression the existing site gave was wrong.
The new design is certainly a step in a new direction, but again there is a number of problems with it. First, know your audience - who are your target users ? Let's assume I was right that it's the people like myself - crypto-savvy techs in a need of encrypted backup. What would I like to know first if I stumble upon your site ?
1. How it works
2. How much it's going to run me
How it works - specifically, and most importantly, are you reliable ? It is quite obvious that tarsnap is a one-man show, so you
must convince me right there that you
are reliable. I.e. if you get hit by the bus, will I still have my data ?
Little digging on the site (that I did only because you asked to review the site, and would've not probably done otherwise) revealed that the data is stored on Amazon's servers. Good. Next question - does my data go directly to the Amazon or do you proxy it ? If it's former, then why do I need tarsnap as a service rather than a simple client product that handles data gathering, compression, encryption and uploading to Amazon ? If it's either, then, again, the issue at hand is tarsnap being an additional point of failure on route to my data (should, god forbid, anything happen to you or the company).
Assuming the data goes straight to Amazon, I will be happy to use your service just not to deal with the Amazon directly. What I need is a re-assurance that the data is recoverable, should tarsnap cease to exist.
To sum this part up - all of the above needs to be on the front page, or at the very least - one click away from it under an obviously labeled link.
Second point - how much is it - is equally important. The "picodollar" term as ingenious and geeky as it is needs to go. It is something that detracts the attention from other information on the page. I am reading the text, bam, picodollars, I keep reading, but I am actually trying to remember what power the pico is. So anything that I read after the picodollars doesn't really digest.
Additionally, the cost calculator is a must. Say I have 60GB of data to backup. Let me punch it in on the page and show me how much it would cost to run the initial upload and how much it's going to be monthly. Also an estimate of an initial upload time would be very handy to have. If you are on Shaw like me, the 50 KBps upstream bandwidth is not exactly online backup friendly.
Lastly, design-wise. It is not bad, but it is pretty far from being great. You clearly have a preference for a clean looking site, and I think this is an absolutely correct (visual/brand) positioning of the product. However neither the existing nor the new site are it. The site can be clean and appealing to the tech crowd and not look like it was designed for the Lynx browser. Have a look www.minimalsites.com, lots and lots of great examples of truly minimalistic, clean and light looking sites.