You can get a lot of info by googling "limbal relaxing incisions." According to what I've read, they can eliminate about 50% of preexisting astigmatism on average, with some variation. Not all cataract surgeons are experienced doing this procedure, so it would probably be a good idea to inquire beforehand. It can be done at the time of catarct surgery, and many surgeons don't charge an additional fee. I don't think there's much risk invovled with an experienced surgeon. In my case, most of my previously mild astigmatism was eliminated.
In the clinical trials, AcrySof toric IOLs did a somewhat better job of correcting astigmatism than LRIs. However, there have been some posts on this forum about bad results with these new toric lenses. (Maybe the surgeons were inexperienced, who knows?)
The most reliable way to correct astigmatism is supposed to be LASIK/PRK. There are two downsides to these procedures, IMO. (1) They cannot be done at the time of cataract surgery; I believe you have to wait a couple of months. (2) There's sometimes a rather hefty out-of-pocket fee.
Little to add to JodieJ's comments. Use the search feature and archives also as we've discussed LRI many times.
JCH III MD