memory - "Faster" RAM at lower clock speeds?

I've been kind of interested in the mechanics (er, electronics) of computer systems lately and after a bunch of research and looking at my computer's properties, I've come across something strange.

Most people say faster RAM means, well, faster RAM. Sounds logical right? But after looking at my computer I noticed that my installed RAM is capable of being under clocked. It usually runs at 333 Mhz (DDR2 at 667) with a 5-5-5-15 timing. However one of the programs I'm using to look into my PC says that it is capable of working at 266 Mhz with 4-4-4-12 timing and 200 Mhz with 3-3-3-9 timing.

The thing is, according to my calculations (simply the timing number divided by the clock frequency to get latency in seconds), 200 Mhz at 3-3-3-9 timing actually has better latency than 333 Mhz at 5-5-5-15 timing.

So my question is: Is this in fact true that I can actually improve the performance of my system if a program I run is accessing the memory in a truly random fashion (as opposed to sequential read/writes) by under clocking the RAM and selecting a tighter timing or have I made an error somewhere?

Edit: Just before you start arguing that I'm mistaken about RAM "speed", let me define what I mean by "faster". RAM has both latency and bandwidth. When I say "faster" I am strictly talking about latency and not bandwidth. In sequential read/writes, yes, bandwidth is much more important than latency (RAM operates in burst mode, which achieves it's maximum bandwidth by pumping sequential rows of data into CPU cache even if the CPU never asked for the extra stuff). In random access however, latency totally out rules bandwidth.

So my question is: Is this in fact true that I can actually improve the performance of my system if a program I run is accessing the memory in a truly random fashion (as opposed to sequential read/writes) by under clocking the RAM and selecting a tighter timing or have I made an error somewhere?

This is hard to answer as there are many variable to consider. In theory you should be able to improve performance of just those programs. This assumes that memory is highly fragmented or you are reading/writing small amounts of data. Also note that your overall system performace may degrade. Best thing to do is give it a try as it is a very simple test assuming your BIOS provides access to those settings.

This pretty much goes over it http://www.pcstats.com/articleview.cfm?articleID=873

Typically, you'd gain more benefit by higher MHz vs. lower CAS timings. In a general case, even though your CAS timings may be increased to 5-5-5-15 from 4-4-4-12, for example, the extra 133MHz of clock speed gained will allow the memory to go through those CAS cycles in less time, thereby being "faster" in terms of random access.

However, it seems that you've stumbled upon an edge case where the lower CAS timings take less time than the higher CAS timings, despite the lower clock speed. In theory, I suppose that a 100% random workload would perform better in this scenario if your math works out. But like others have said, there are other factors to consider (motherboard, etc.), and this would only apply for an entirely 100% random workload that only reads a single word at a time. For the case that you defined, the difference is marginal as it is. Anything aside from that hypothetical random workload would have less performance than if it were running with the RAM modules at a higher clock speed.

In the real world, when there's a tradeoff, go for the higher MHz (or registered modules, or whatever applies to your need).