According to this answer (and a number of other discussions on the web) one does not say tachanun during the mincha on the day before the relevant simcha-day.
Would this include a case where a baby is scheduled to have a bris the next morning?
[this then begs a question regarding the "simcha" vs. "kedusha" of the day of a bris so I can consider whether a month with 15 bris days would obviate tachanun on the rest of the days]