A good note is short, specific and easy to act on. Most bad ones are long, general, and ask the reader to do the work of figuring out why you are relevant.
Short enough to read on a phone without scrolling. If it needs a scroll, it needs cutting. Attachments on a first contact trip spam filters and rarely get opened — link instead.
One follow-up, a few days later, is reasonable and often what gets the reply. Two is the limit. Stop immediately on any reply, and stop on a bounce rather than retrying — repeated bounces from one sender degrade deliverability for every message you send afterwards.
Flattery about the company's mission, a restatement of your résumé, and anything that reads as generated. The reason a personal note works is that it is evidently personal; the moment it does not read that way, it performs worse than not sending one.
From your own history and the role's description — yours to edit before it sends.
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