Please look into the alias definition. Perhaps there is a regular expression, matching to "wet" but not "wett". Furthermore you should experiment with the options "Stop search on exact alias match", "Stop search on regex alias match" and "Score non-contiguous matches".
The history is already persistent among restarts. Just booted my machine, all entries are still there. Some options regarding the history is available at "Search Behavior" (just in the case you didn't see it yet).
If you don't want to enter the modifier each time, you can create a new alias which uses dosearch or restartsearch (see help file for more information).