The 1787 "Laughing Head" Connecticut Copper is such an unusual design type that it is listed separately in the Redbook (Guidebook of United States Coin). The nickname came from the crude rendering of a regal portrait whose parted lips appear to be laughing. There are actually two different obverse dies that qualify as "Laughing Heads". Miller's 6.1 obverse is the more common, while his 6.2 obverse is more rare. Because of subtle differences, the 6.2 obverse appears to be "laughing" more than the 6.1. Both obverse dies are paired with the same reverse (Miller's "M").
This is a fairly plentiful type and there are numerous high-grade examples. The finest examples are two Mint State pieces: one from the Garrett Collection in 1980 and a more recent example from the Eric Newman Collection. Below those two coins are numerous AU pieces that fill out the rest of the Condition Census.