Last weekend I explored tip rails some.  What I am about to document 
here is not new, but I think it is the first time it has been written 
down in public.

Machine faced mouthpieces usually have curved facings that extend all 
the way to the tip of the tip rail.  This gives a slight arched 
appearance to the rail when viewing the end.  Hand finished 
mouthpiece can be the same, or have a flattened tip rail, or have a 
flip-up on the tip.   I have done most of my facings with a flattened 
tip or only slightly curved.  They are the freest blowing.  

I was trying out a tenor Lakey 6*3 and noticed it had superb high 
altissimo (but the rest of the sound was so-so for me).  It was 
especially responsive in the G4-C5 range that I normally can not get 
at all (normal high F = F3).  It has a very thin tip rail, a somewhat 
sharp tip, and a flip-up tip rail.  I've had other pieces before with 
the flip-up, but I never noticed good altissimo. Perhaps I did not 
look hard enough because they had more significant problems.  I 
always thought they played better when I refaced them and removed the 
flip-up.

So, I added some flip up to a diamond inlay Beechler I've been 
working on for kicks (I had previously put a bullet chamber in this 
piece).  Viola, instant high altissimo!  It also added some 
resistance to the piece overall, but it was a moderate tip opening to 
begin with.

It is tough to gauge tip rail work.  I just did it by eye with a good 
light source.  You can tell by how the light reflects off the rail 
whether it is flat, curved slightly or has more of a flip-up.  Adding 
more flip-up also involves reshaping the tip rail by filing the end 
and/or relieving the baffle some.

I then went to several of my back-up mouthpieces that I felt was a 
little too closed for me and added some flip-up.  The plan was to add 
resistance to them and get high altissimo.  This worked great.  I'm 
going to start using them and see if they work well on gigs.

I don't get many solos where I can play a lot of altissimo.  The few 
times I do, I go for it and it's sometimes not there.   My chops are 
too loose, the reed has gotten soft and I'm blowing too hard.  It 
will be interesting to see if it is there now when under fire.

Jon Van Wie has commented that for altissimo, some players like the 
rail flat, some like it curved up.  I do not see how flat is better 
for altissimo response unless the flip-up make some players overshoot 
the lower altissimo notes.   It is possible that flat may give a 
sweeter tone to the altissimo, but relieving the baffle near the tip 
rail sweetens it up fine enough for me.

So if you have a backup piece that is a little small for you (could 
stand some more resistance), give it a shot!  Let us know if you get 
similar results.