Try making the length of Str1 much larger then you need it to be -- I don't think it's easy to change the size of a constant after it's declared.
Copy("The next string",Str1,15)
Alternatively, you could use either a buffer (like L1, L2, etc.) or an appvar.
This might not work/probably needs tweaking, but try something like:
(The  adds a null byte, just in case)
Also, I'm trying to remember -- if you compile as an app, can you rewrite program memory like Str1 or Pic02?Edit:
Changed 'Zero(pointer,size)' to 'Zero(size)->pointer'