reciprocal links

I have an established site that is already ranking highly for some keywords. I want to keep increasing the authority of the site by building more (safe/whitehat) backlinks. One option I've been looking at is link exchanges. Is this a good idea or not? The linking sites would all be highly relevant to the niche I'm targeting.

I think so that, it's a good idea. Cause you said, its highly relevant site. But footer linking is not a good idea. Google can read that kind of links. You can exchange, but trickily. That will be better.

Those kind of links have a bad reputation but I also heard they can work well when done right.

Reciprocial linking is somewhat sub-optimal. What you can do is build another site for linking back. Say, a blog with some good articles. You can say that you can link from an article on this blog to their site. That way, you give them a link and it is not reciprocal.

Most webmasters/editors of other sites only know that a link is good, but they don't care where it comes from.

A reciprocal link is an agreement between two webmasters to provide a hyperlink within their own website to each other's web site. Generally this is done to provide readers with quick access to related sites, or to show a partnership between two sites. Somehow it will add bad reputation...