Deposit before seeing the Blepharoplasty schedule

I am comparing two clinics for Blepharoplasty and the price is not the only thing confusing me. One clinic wants a deposit this week but only sent a general timetable, like consultation one day and surgery the next. The other clinic gave a slower answer but named the hotel area, transfer time from airport, and said I would get the exact schedule after the surgeon checks my photos. I do not expect certainty before arriving, but I feel uncomfortable paying when I do not know if the follow-up check is included before my flight home. Did anyone ask for this in writing before deposit? Maybe I am being too cautious, but the eyes area makes me nervous.