Forgot How To Do This In SQL

I am having a serious brain f@rt right now. I am querying a table full of customers, dates and payment amounts

 I am looking to get each customer, the most recent payment amount and most recent payment date.

 

SELECT Customer, MAX(TranDate) As TranDate, TranAmount GROUP BY Customer, TranAmount

 ...gets me the following:

customer1      9/14/2007   100.00

customer1      9/14/2007    50.00

customer2     9/1/2007       75.00

The problem being that each customer has multiple payment amounts so when I GROUP BY the TranAMount column I am getting multiple rows for the same customer. I am looking for a single row or customer, date and amount for each customer. What am I forgetting?