Michael Kinsley does it perfectly in this 1975 letter to the New Republic.
This is an inquiry about a summer job. I wrote to Marty Peretz, who is a former teacher of mine, several months ago, but received no response. Under the assumption that he is a busy man I have declined to take a hint, and now write to you. A resume and some samples are enclosed. They are mostly humorous (at least in intent) but, as the resume indicates, I have written serious pieces as well for various publications and have a Nader book coming out in the fall whose tone could best be described as morose. Friends at TNR might be willing to put in a good word for me: Tom Geoghegan or Eliot Marshall among the old guard, or Linc Caplan among the new. Tom and I were roommates for two summers while I was working for Nader and he was working for you. I know Ralph would vouch for me, and I hope Marty would as well. Thanks very much.