How can we improve upon Bitcoin's highly concentrated coin distribution?

Only the top 3% should be power-law concentrated, the rest distributed with diffuse gas random concentrations:

"Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States" by A. A. Dragulescu and V. M. Yakovenko

We shouldn't give coins away to the lazy who do nothing to earn them, because Risto explained that in Russia the recipients just squandered the gifts.

Ideas thus far:

1. Decentralized CPU-only proof-of-work, but the threat are botnets

2. Centralized premine then distributed with a faucet first-come, first-served until depleted.

3. Centralized premine then distributed to merchants every month or quarter evaluated to be bonafide. So this really requires hiring staff, which should be paid either from premine or a foundation with membership fees.

Hit me with ideas please!

I will keep self-moderation to an absolute minimum but please try to stay on topic and no ego battles.