Isearch - Incremental search with predefined initial character?

[BobD]

Using  24.3.1 (i386-mingw-nt6.1.7601)

I wish to do incremental searches with the first character pre-defined, i.e. 
have emacs prepend a character to the characters I enter.

E.g., if I start an i-search, and then enter "abc", emacs will pretend I 
entered "Xabc".
If I continue the i-search, emacs will seek "Xabc".

I fiddled with isearch-mode-hook, but I couldn't see how to continue searching 
with the prepended character.

Do I need to fiddle with the "isearch-repeat-..." code?
Do I need to fiddle with other code?