It is well-known that cover letter should demonstrate interest to the targeted company:

"simply put, no the point of a cover letter is to articulate why you will be valuable to my company and how. a generic one shows the opposite, if the content isn't specific to the job I have open for you by definition it is not good, waste of my time and will get put in the trash before I ever get to your actual resume"

°

"keep it as brief as possible and as specific as possible about why you really are interested in THIS company and THIS position rather than any of the other positions that you qualify for at other companies."

However, It turns to be difficult when the targeted job field is present in near every company (because all companies have computers), and you start to apply to positions without descriptions (this also include jobs without advertisement).
In my case, while most companies outsourced the process, most opportunities still comes from companies which haven't done it.

So, how to make cover letter company specific in that case, so they aren't a redacted copy of the resume?