Word or idiom for a small group of birds

Looking up online, I realized there are quite a few different words for groups of birds. For pigeons, a group would be a flock or a flight, while for falcons you would have a cast of falcons.

But, what about nouns that give some information on the number of birds? Is there, for instance, a word signifying a small group of pigeons? Or just a small group of birds.

The word I would use is covey. As the following citation shows, covey can be used as a word for a small group of birds: Oxford Living Dictionaries

a small flock of birds, especially partridge.

The same source gives many example sentences using coveys, meaning small flocks of birds, of which the following is one:

...both species form coveys, which are flocks of 4-6 fused family groups.

Somewhat whimsically, you could use the names of various subdivision of a military air force. According to Wikipedia, for the U.S. Air Force, these subdivisions are:

• Detail (2-4)
• Element or Section (5-20)
• Flight (20-100)
• Squadron (100-300)
• Group (300-1,000)
• Wing (1,000–5000)