The common name of "Copper tetra" is given to at least 3 different species. Can you look up "Copper tetra" to see the scientific name of the type that you have?
If it is Hasemania nana aka "Copper tetra" or " Silver tip tetra" this type of tetra can be moderately to severely aggressive to con-specifics in aquarium. Especially if you have a high ratio of males to females.

 

So as the shop label says, I have "hasemania marginata", if that helps...

 

The common name is Silver Tip tetra.
Too much coffee? Or, maybe, because of overcrowding.

 

Damn... So moderately and more agressive. That fits.
Overcrowded? 20 tetras?
Well, what to do now? Based on coloration and size, I would say I have 4 males and 6 females. Shall I try to catch some of the males and see what happens?

 

You could try decreasing the male to female ratio- this may work. But, for aggressive tetras it is better to put them in a larger tank and increase numbers to disperse aggression. I think the problem, in your case, is both too little space in 20 gallon to mark territories and not enough numbers to spread out aggression more evenly..

 

Blue tetras (Knodus borki) might be tough enough to stand up to the silvertips.

 

Ok, I guess I got the point. I will try to reduce the males first...
Thank you all for helping me.

 

Tetras are schooling fish and as with other schooling fish they have a "pecking order". (learned the hard way). Schools are thought of to be as "one". They, as in the wild, need larger spaces, vegetation for hiding (if the school is not large enough) but eventually the top dog will or may take all others out. He/she is not a "bastard" but in an improper environment. I bred some innocent little "lamp eyes" which are a schooling fish - all were gone save for the top dog. Got a 100 gallon, added enough for a large school (about 50) and all was well. They were so happy they bred and I was able to trade them for plants in NYC's Chinatown.

They, as with people actual produce stress hormones (adrenal/cortex) and it is in the water. A long time ago there was a Youtube video on the Amazon and other huge river systems where many of our aquarium fish come from - in their native environment of course. The schools are HUGE and vast! Thousands often.

Bump: As other's have noted a 20 gallon is just too small - small fish do not translate to small environments.