To cause something to fall or descend gradually through a sieve or similar device. She sifted down the flour into the bowl to ensure there were no lumps.
To examine or sort through something carefully in order to isolate what is most important or useful. He sifted down the documents to find the relevant information for the report.
In computer science, particularly in heap data structures, to move a node down the tree to maintain the heap property. The algorithm will sift down the node to restore the heap order after deletion.