How to avoid nested function definitions and still use

How to avoid nested function definitions and still use

Suppose I have these two functions:
fInner<-function()
{
# Do some complicated stuff, and...
I<<-I+1
}
fOuter<-function()
{
I<-0
fInner()
print(I)
}
Calling fOuter() produces an error: Error in fInner() : object 'I' not
found. I know, that one way of fixing it is to re-write the example into
fOuter<-function()
{
fInner<-function()
{
I<<-I+1
}
I<-0
fInner()
print(I)
}
But what if I don't want to nest the functions that way? In my case fInner
is a very heavy and complicated function (which I might want to move into
my library), and fOuter is really an ad-hoc created function that defines
one iterator. I will have many fOuter-class functions in my code, so
nesting them will require duplicating the fInner inside every single
little one iterator definition.
I suspect the solution has something to do with environments, but I don't
know how to do it. Can anyone help?