Letter Paragraphs: Professional letter paragraphs should be relatively concise. The first paragraph may include a brief friendly opening and a concise explanation of your reason for writing. The second paragraph (and any subsequent paragraphs) should expand upon your reason for writing. The final paragraph should restate your reason for writing and, if applicable, state your plan of action (or request some type of action be taken by the reader).
Remember, you're hoping the person who receives your letter has no memory of your closing at all. The last thing you want is a hiring manager going into an HR meeting with your cover letter in hand, asking the team if they want to meet with "Mr. Kindest Personal Regards."