Shiren 1 DS:Deep Sleep

Effect on Monsters

Monsters will be Asleep for 14 normal [[Speed] turns, then will wake up and permanently be Hastened by one level.

Reading a Scroll of Sleep will inflict this status on monsters.

Transforming the monster by successfully throwing Monster Meat at them. Presumably of a monster that does not not normally move at high speeds.
Having the monster trigger a Slowness Trap as a Trap Master or as a Mecharoid Family Monster, or successfully throwing the Trap at the monster. Floating-type Monsters cannot be affected by traps before reading a Super Trap Scroll on the same floor.

A Trap with a Sealing effect such as a Curse Trap or Unequip Trap will not decrease a hastened monster's speed.