Create a new list from selected items in another list

Hi All--

I have a list which contain variables 0s at the end of each vector on
the isit. I want to create a new list with only numbers > 0.
It seems simple, but i tried several option, none of which worked.

CCC <-  list(A=c(1,2,3,0,0,0,0), B=c(2,3,4,5,0,0,0,0,0,0))

for (i in 1:length(CCC)) {
  for(j in 1:length(CCC[[i]])){
    if(CCC[[i]][j]>0)
    BBB[[i]][j] <- CCC[[i]][j] #BBB <- AAA
    }
}
 desired output is
$A
[1] 1 2 3

$B
[1] 2 3 4 5

Thanks-EK