Gave $30k as a married couple from a joint account, do I need to file Form 709?

Last year I transferred $30k from our joint bank account to our adult son's bank account to help with his house purchase. I was mindful of not exceeding the $15,000 annual gift exclusion amount per giftee.  We considered it as $15,000 from each of us, and so qualifying for exclusion.  Do I 1) need to fill out Form 709 indicating that this was a split gift from a married couple?  2) does the Form 709 need to specify the amount, or can I stop at Part I, line 18 which is the signature of the spouse to consent to gift splitting?  The rest of Form 709 seems to deal with Tax computation for the gift, which we do not owe.

This year I intend to give another $30k joint gift to an individual , but will write two separate checks for $15k signed by me and the other check signed by my spouse.  Will the separate checks (but from same joint account) negate the need for filing a Form 709 for gift splitting?