Collected gaits - A horse is collected when he brings his hind legs far enough under his body (engages) that they carry more weight than his forelegs.  In order for a horse to do this he has to first be strengthened and suppled by correct work.  A horse that is strong enough to collect may be asked to do so by half-halts, transitions or a combination of them.  But, if you ask horse that isn't strong enough to collect, to perform half-halts (which are by default collecting exercises) than you will always fail and your horse will become less engaged in time instead of more engaged.