Delete duplicates - T/SQL

Hi,
Can anyone help please? I have some code which gets a list of duplicate records. I want to be able to delete one of the records and leave the other. However so far my code deletes all records. Can anyone tell me how I select just one of each pair to delete? It doesn't matter which one of the pair goes.

delete
FROM Sickness
WHERE (staff_id IN
(SELECT [staff_id]
FROM [Sickness] AS Tmp
GROUP BY [staff_id], [start_date], [end_date]
HAVING COUNT(*) > 1 AND
[start_date] = [Sickness].[start_date] AND
[end_date] = [Sickness].[end_date]))

Thank you!

Here is the solution to the above problem, if anyone is interesting.

/* Script for deletion of Duplicate record from the Sickness Table */

<<Declare @payroll varchar (8),
@staff_id int,
@start_date datetime,
@end_date datetime,
@sickness_code int,
@cnt int

Declare getallrecords cursor local static For
Select count (1), payroll, staff_id, start_date, end_date, sickness_code
from sickness (nolock)
group by payroll, staff_id, start_date, end_date, sickness_code having count(1)>1


Open getallrecords

Fetch next from getallrecords into @cnt,@payroll,@staff_id,@start_date, @end_date,
@sickness_code

--Cursor to check with all other records

While @@fetch_status=0
Begin
Set @cnt= @cnt-1
Set rowcount @cnt

-- Deleting the duplicate records. Observe that all fields are mentioned at the where condition

Delete from sickness where payroll = @payroll and staff_id = @staff_id
and start_date = @start_date and end_date = @end_date and sickness_code = @sickness_code

Set rowcount 0

Fetch next from getallrecords into @cnt,@payroll,@staff_id,@start_date, @end_date,
@sickness_code
End

Close getallrecords
Deallocate getallrecords>>