Why composite indexes ?

Hi, I did a check last night to compare 2 selects using a) an index on one column only, ie. not a composite index (I updated stats HIGH on this column) and b) a secondary column in a composite index (also updating stats HIGH on this column). I used the same column for both tests. The first select was immediate, but the second select, even though I was using an index, took long before it returned a result. My question is, why do I use composite indexes if it is faster to select on indexes created on one column only ? Our database was created with lots of composite indexes. Regards Dirk