Counting Dyck-like Paths?

Question

Dyck paths count sequences of $n$ 1's and -1's s.t no sub-sequence from the left side has a negative sum. Suppose we instead have the restriction that no sub-sequence from the left should have sum greater than $U$($0\leq U \leq n$) or less than $L$($-n\leq L \leq 0$). Is there a known way to decompose this counting problem?