Defend the weekday, because federal law gives the weekend nothing. The Department of Labor's overtime fact sheet says the FLSA requires no overtime pay for work on Saturdays, Sundays, holidays or regular days of rest, as such, and requires time and one-half only for hours worked beyond 40 in a fixed and regularly recurring 168-hour workweek. Your Tuesday off is worth exactly what a Sunday off is worth, which means the whole job is putting the right things on it. The condition that changes the plan is a roster you cannot see yet: when the schedule is not posted, the first thing to secure is the posting date, not the day.
Weekday-only business goes first
Some things exist only between 9 a.m. and 5 p.m., Monday to Friday: the dentist, the bank branch, the county clerk, the school office, the parts counter. Those get the first slots on the weekday off, because they cannot be moved to the weekend at any price.
Everything else is negotiable, and it competes with what you want from the day. Book the immovable appointments first, in the morning, and leave the afternoon as one block rather than three fragments; booking an appointment around an inflexible shift is the same sorting done one appointment at a time.
Federal sites hand you a few free weekdays a year. The National Park Service's passes page lists fee-free entrance days for 2026 on February 16, May 25, June 14, July 3 to 5, August 25, September 17, October 27 and November 11, four of which fall midweek: Tuesday August 25, Thursday September 17, Tuesday October 27 and Wednesday November 11. A weekend worker is the person best placed to use them, and the rest of the day's costs come down the same way.
The notice rule decides how far ahead you can plan
A weekday off you learn about on Thursday is not a plannable day. In Oregon, the state's predictive scheduling rule requires employers in retail, hospitality and food services with at least 500 employees worldwide to give the written schedule 14 calendar days in advance, to provide a written good faith estimate of median expected monthly hours at hiring, and to pay one hour at the regular rate when they add more than 30 minutes of work or change a shift's timing. It also sets a 10-hour break between shifts, with work inside that break paid at one and a half times the normal rate.
Check what your own state or city requires and write the posting date in your calendar as a recurring entry. Then the question you bring to your manager is about the date, not about fairness, and a request for more predictable hours starts from the same number.
One worked example: a Tuesday off at 32 hours
Example, with the fact sheet's own arithmetic beside it. The overtime fact sheet works a 45-hour week paid $405 as a $9.00 regular rate, with $22.50 of extra overtime pay due. Run your own week the same way.
You work Friday to Monday, four 8-hour shifts, 32 hours at $19 an hour, which is $608. Tuesday is your only weekday off. Your manager offers 8 hours on that Tuesday: it brings the week to 40 hours exactly, so every one of those hours pays straight time, $152, with no overtime premium. The 41st hour would be the first at $28.50.
That is the trade in one line: $152 before taxes against the only day the dentist, the bank and the county clerk are open. Take the shift when the $152 is already spoken for; keep the Tuesday when two of those errands have been sliding for a month, and apply the same sort to whatever else lands on the day.
Two messages, both with a date in them
To the manager, before the roster goes up: "I'm at 32 hours Friday to Monday. I keep Tuesdays clear for appointments that only book on weekdays. If you need a fifth shift, Wednesday works." That names the hours, the reason and an alternative, and it arrives before the schedule rather than after it.
To the person you want to see: "I'm off Tuesday. Free after 1 p.m., once the 9:30 dentist is done. Lunch at 1:30?" Weekday friends have weekday constraints of their own, so the hour matters more than the enthusiasm.
Then put one line in the calendar for the day itself: "Tue: dentist 9:30, bank by 11, free from 1 p.m." Three entries, two of which cannot happen on a Saturday, and an afternoon that is yours because it was written down before anybody asked for it.