I partake in British Parliamentary Debate. A good argument:

1. Is structured like an essay: tell what are you going to tell, tell it, then tell what you just told.
2. Consists of a description, elaboration, and an example.
3. Elaboration consists of a chain of logic that starts at the position being defended and terminates at a terminal value.

A counterargument either:

1. Attacks the premises or a link in the chain of logic and shows that the argument leads somewhere other then the terminal value.
2. Proves that the terminal value isn't actually terminal.
3. Constructs an alternative argument that leads to an even more important terminal value and does so to make it and the original argument mutually exclusive.

A good counter argument is concise.

For example: this house would force everyone to publish their income on the Internet.

This motion would lessen corruption by crowdsourcing police. Any person could go online and compare their neighbor's apparent wealth to their stated income and raise an alarm should a disparity be found. The neighbor would of course know this and thus would not dare evade taxes or whatever. So we have less corruption, less people in jail due to deterrence, more taxes, and less strain on our actual police!

Attack premises: most people live in big cities in relative anonymity, neighbors don't know each other, and wealth isn't conspicuous.

Attack logic 1: government websites are hardly a popular destination. People simply wouldn't care to go through tables of numbers.

Attack logic 2: people would just spend their ill gotten gains inconspicuously. (counter-counterargument: wealth is about signaling status which must be visible)

Alternative: this is a huge infraction on people's privacy which is more important than lessening corruption. (This one should be more elaborate but I'm out of steam.)

Note though that British Parliamentary Debate is about winning and not truth.