Instead Of Update Trigger W/ Self-Referencing Table

Setup:
Using SQL 2005

TableA

ID INT PK
Name VARCHAR
RefID FK
ID Name RefID
1 Test1 <NULL>
2 Test1a 1
3 Test1b 1
4 Test1b1 3
5 Test1b1a 4

CREATE TRIGGER Update_ID
ON TableA INSTEAD OF UPDATE
AS
IF UPDATE(ID)
BEGIN
DECLARE @old_ID INT
DECLARE @new_ID INT

SELECT @old_ID = ID FROM DELETED
SELECT @new_ID = ID FROM INSERTED

UPDATE TableA
SET ID = @new_ID
WHERE ID = @old_ID

UPDATE TableA
SET RefID = @new_ID
WHERE RefID = @old_ID
END

SPROC:
UPDATE TableA
SET ID=6
WHERE ID=2



RefID is the FK to ID
ID is also the PK to another table and has the relationship use cascading Delete and Update.

Problem:
"The UPDATE statement conflicted with the SAME TABLE REFERENCE constraint"
This is referring to the first UPDATE of the Trigger.
It was my understanding that Instead Of checks the constraints after it is all done yet it errs with the first Trigger UPDATE.
I was expecting to overcome the self-reference constraint issue by using Instead Of and with the first Trigger UPDATE, change the ID(PK) and then change the RefID(FK) with the second Trigger UPDATE.
Once that was done, it should have not had any constraint problems. Thoughts?

Thanks, Nathan