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My case it not quite that an incorrect page is ranking. It is the right ones, but I want to change the URL for these pages to optimise that part also, since the keywords are not included in the URLs right now.

Good question, one that I don't feel like gets addressed enough. Yes, you should always include self-referring canonical tags. There's a few reasons for this, but primary it helps one version of your URLs get indexed. Here's a handful of cases where they're helpful: Some CMSs create URLs that are case-sensitive - i.e. URLs will resolve at /Some-page, /some-page, and /Some-Page HTTP vs. HTTPS - if you've gone secure, self-referring canonical tags can help search engines learn your new structure and drop HTTP URLs from the index quicker, or at least prevent both secure and non-secure from being indexed Absolute/Relative links - some development teams prefer to use relative URLs in links when working in Dev and Test environments, this is helpful for preventing unwanted Dev/Test URLs from getting indexed, but isn't ideal for SEO. This is where self-referring canonicals come in. WWW vs. Non-WWW - another safeguard to prevent indexing of both versions, even with redirects in place, it doesn't hurt to have a fall back URLs with Parameters - If your site appends parameters to URLs for any reason, self-referring canonicals will prevent indexation of /this-page?q=123 There's probably other reasons to add to this list, but these should be compelling enough to go ahead and add them.