MAX Date Query - How To Have A 'unique' Date?

My database holds details of visits made to customers by support staff.
I am running a query which returns details of the last visit made to a customer as below with results displayed on a webpage.

SELECT Visits.Date1, customers.CustID AS customers_CustID, customers.Customer, Visits.CustID AS Visits_CustID, Visits.Visitee, Visits.VisitType, customers.RegionID, customers.NextVisit, customers.NextVisitBy, customers.Confirmed
FROM customers INNER JOIN Visits ON customers.CustID = Visits.CustID
WHERE (((Visits.Date1)=(SELECT MAX (Visits2.Date1) FROM Visits AS Visits2 WHERE Visits2.CustID = Visits.CustID)))
ORDER BY customers.RegionID, customers.CustID

SELECT MAX on Date1 is used to select the most recent (largest) date. The problem I have is that if 2 different staff members visit the same customer on the same day, the query logically returns 2 MAX date results for that customer, whereas I only want 1 result per customer. As the dates are the same I am not sure how to proceed. It doesn't matter which of the 2 results are returned. Does anyone have any ideas? Thanks in advance :)

ps - I can't perform MAX on the VisitID as the support staff don't always enter the visit data in the correct order meaning that an older visit date might have a higher VisitID than a more recent visit.