Transact SQL :: Server Reference Field From Adjacent CTE

I am trying to eliminate a scalar function by rewriting a view. I currently have a structure similar to the following:

With FirstQuery as (SELECT Trial, SBOI, TBOI,
FROM TU
WHERE SBOI Between 22000 and 22999 and TBOI < 10000),
strt as (SELECT TOP 1 TimeOfEvent, Trial, SBOI, TBOI
From TU ORDER BY TimeOfEvent),

[Code] ....

What I trying to do is for the Trial, SBOI, and TBOI in FirstQuery, find the Start Time and Stop Time. TimeOfEvent is an integer in milliseconds. Say I have the following data:

TrialID     SBOI     TBOI     TimeOfEvent
A             22000   5000     5
A             22000   5000     10
B             22000   5000     8
B             22000   5000     15

So the DISTINCT output would be:

     Trial     SBOI     TBOI     StartTime     StopTime
     A         22000   5000     5                  10
     B         22000   5000     8                  15

The problem I am having is that strt is selecting the smallest time period. It doesn't seem to care what the current record in cte is. I thought that by using my joins, it would make it select smallest TimeOfEvent for the Trial, SBOI, and TBOI that are selected in cte. Obviously that is not the case. So, I was trying to add a WHERE to the strt Select Statement such as 

WHERE TrialID = FirstQuery.TrialID and SBOI = FirstQuery.SBOI and TBOI = FirstQuery.TBOI but it isn't working either.

What can I do?