Entries are arranged in hash tables with storage for multiple entries per bucket with entries being shifted among hash tables to make room for entries being added. A path is determined through a search of the hash tables to identify where to move entries during insert operations among the hash tables to make room for a data item being added. Entries are moved and a data item added according to the identified path. Many different types of searches may be used, such as breadth-first, depth-first, random walk, etc. Also, a free position at the end of the path may be identified by being a bucket having a lowest occupancy level in a first predetermined number of levels of the search, a first bucket encountered having space available or an occupancy level less than a predetermined threshold level, with the predetermined threshold level typically being less than that of a full bucket, etc.