Sometimes pragmatic constraints will leave you with two options. A short cover letter or no letter at all. In that case you could use a quickie letter like one of these.
Mr. Tom Jones
Yo- Yo Products, Inc.
3 Bay State Center
Chicopee, MA 01006
Dear Mr. Jones,
My neighbor, Myrna Olde, told me that your assistant at Yo-Yo Products is plarming to retire soon. Good people are hard to replace. Could we discuss the possibility that I might be a good successor? I will call you next week to see what you think. In the meantime, my resume is enclosed for your review.
The cover letter adds to your attractiveness as a candidate in three ways.
Highlighting : You can give those positive characteristics of greatest interest to a particular employer more prominence in the cover letter than you did in your resume.
Reframing : Through your cover letter, you can put some of your experiences in a frame of reference that more closely meets the needs of the employer.
New material : Your cover letter can include material of interest to an employer that would be difficult to present in a resume. Your motivation for wanting to work for that particular company is an example.