How do I count occurrences by day in SQL?

Newbie SQL question here -->

I've got an Occurrences table that contains a 开发者_运维问答row for each time a user did something. A user can do the thing multiple times per day. It looks like this:

Date      Username
------    --------
1/1/9     User1
1/1/9     User1
1/1/9     User2
1/2/9     User1
1/2/9     User3
1/3/9     User1
1/3/9     User1
1/3/9     User1
1/3/9     User2
1/3/9     User3

I want a query to simply return the Username and the quantity (count) of unique days they appear. For the above data set, the result I'm looking for would be:

Username    UniqueDaysAppeared
--------    ------------------
User1       3
User2       2
User3       2

I keep getting screwed up because my query is returning not the count of unique days per user but rather the number of occurrences of the user overall.

SELECT Username, COUNT(DISTINCT(Date)) AS UniqueDaysAppeared
FROM Occurrences
GROUP BY Username