The optimal length-limited Huffman code will encode symbol i with a bit string of length hi.
The canonical Huffman code can easily be constructed by a simple bottom-up greedy method, given that the hi are known, and this can be the basis for fast data compression.
However, the original paper, "A fast algorithm for optimal length-limited Huffman codes", shows how this can be improved to O(nL)-time and O(n)-space.
The idea is to run the algorithm a first time, only keeping enough data to be able to determine two equivalent subproblems that sum to half the size of the original problem.
[1] Many other improvements have been made to the package-merge algorithm to reduce the multiplicative constant and to make it faster in special cases, such as those problems having repeated pis.
[4] Methods involving graph theory have been shown to have better asymptotic space complexity than the package-merge algorithm, but these have not seen as much practical application.