Hi

For some reason, when I was first learning the rules, I got the impression that the runner can only boost the strength of an icebreaker before doing a run, and not after the corp has rezzed a piece of ice. But now I can't find that in the rules. Was I wrong?

Thanks

Your answer is really in the timing chart in the rulebook. After the runner commits to continuing, there is a window in which paid abilities can be used and cards can be rezzed. The corp may rez the ice here.

Then the runner *encounters* the ice, and there is another Paid Ability window, in which icebreakers can interact with ice. Boosting strength is one such Paid Ability, as is Breaking Subroutines.

See "Increasing an icebreaker's strength" on p16, "encountering ice" on p18, and the timing structure diagram on p33. (And the updated version in the official FAQ.)

For the majority of icebreakers, boosting the strength outside of an encounter with a piece of ICE actually results in the strength immediately reverting to its printed value.