Query Help Needed (JOIN)

I have two tables populated during the use of an application to log
user events and application states. They are named "EventTable" and
"StateTable" and the structures follow:

EventTable:

ID EventTimeStep EventID
-- ------------- ---------
1 5 E1
2 22 E2
3 56 E3

StateTable

ID StateTimeStep StateID
-- ------------- -------
1 1 S1
2 39 S2

I want to perform a query that reports the StateID of the application
at the time that each event was logged to the EventTable. The desired
output is:

ID TimeStep EventID StateID
-- -------- ------- -------
1 5 E1 S1
2 22 E2 S1
3 56 E3 S2

I have tried to create a query with an INNER JOIN where the value for
the StateID output field comes from the last row in the StateTable
WHERE StateTable.TimeStep <= EventTable.TimeStep and where I use a
GROUP_BY EventTable.ID to merge the following rows from the join:

3 56 E3 S1
3 56 E3 S2

However, the closest I can get is a query that gives me the wrong
state when applying the GROUP BY clause

3 56 E3 S1

I also think that the queries I have written is slow and inefficient.
Is there a better way to perform this query or is my database design
fatally flawed?

Thanks,

Adam Nemitoff