My understanding is that it's generally accepted among people researching these things that means restriction (like gun control) does reduce overall suicide rates, it doesn't just make people pick a different method of suicide.

From a quick google search https://www.ncbi.nlm.nih.gov/pubmed/22726520

> Although some individuals might seek other methods, many do not; when they do, the means chosen are less lethal and are associated with fewer deaths than when more dangerous ones are available.