Rebuilding an index requires building a new index before dropping the old index, regardless of the amount of fragmentation present in the old index. This means you need to have enough free space to accommodate the new index.
Reorganizing an index first squishes the index rows together to try to deallocate some index pages, and then shuffles the remaining pages in place to make their physical (allocation) order the same as the logical (key) order. This only requires a single 8-KB page, as a temporary storage for pages being moved around. So an index reorganize is extremely space efficient, and is one of the reasons I wrote the original DBCC INDEXDEFRAG for SQL Server 2000 (the predecessor of ALTER INDEX … REORGANIZE).
If you have space constraints, and can’t make use of single-partition rebuild, reorganizing is the way to go.
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