Mimics should try to impersonate containers more frequently than they do. There are a few proposals for accomplishing this in the Dungeons of Doom:

• Have a special case that generates a mimic in each room with very low probability per room; if a mimic does generate it will always imitate a chest or large box.
• When a large box or chest is generated in a room during level creation, there is a small chance it instead becomes a mimic imitating that type of container, replacing the box. However, the chest contents must be carefully discarded to unmake any artifacts that happened to generate inside it.

Both of these only happen on levels where the mimic being generated is within its ordinary level difficulty range.