Small Drupal 7 site very slow

I have a very small Drupal 7 site, maybe 50 pages and a couple of views. It gets few visitors, just me adding content, and maybe 1 or 2 random visitors a day who stumble in.

It is on a shared host.

It is just really slow, sometimes several minutes to load a page. A Drupal 6 site on the same host, which is much more active, doesn't have the problem.

I should also add that the problem is intermittent. Sometimes it is fine for days on end, sometimes it works well for 3 pages than becomes unusable.

The hosting company say it is down to MySQL caching. Is that likely when it is only serving a hundred pages a day?

So far, I have turned on caching, with minimum lifetime of 15 min, expiry of 1 hour. I have disabled the overlay module, and a few others I am not using.

I am using GeShi to do syntax highlighting, which also drags in Chaos Tools. That is the only unusual thing, although not every page uses it.

Any suggestions?

I am seriously considering reverting to Drupal 6. That would involve quite a bit of effort re-creating the structure of the site, but I need to know I am not digging myself into a hole.