The benefits of diversification are vastly overstated. Especially over long time periods, the benefits of buying e.g. your 5 best ideas rather than your 10 best ideas vastly outweigh the benefits of having less volatility. If you have time to do the research, do this: find companies that are either the low-cost provider, the most-loved brand, or have special government-protected status in their industry. Examples would be Coca-Cola, Wal Mart, Kraft, etc. Possibly, rule out companies whose managers make irresponsible financial decisions (like over-leveraging at a bank, or buying back stock at high prices like Coca-Cola). When these stocks are cheaper than the broader market, buy them. If one of them rises enough that, after capital gains taxes, you're getting more annual earnings per dollar invested in another company of similar or better business characteristics, sell the expensive one and buy the cheap one.
Basically, your goal should be to have a portfolio you don't have to follow, of companies that will tend to grow their earnings faster than their capital and thus throw off free cash for shareholders. If you can get these at a fair price, your net worth should grow nicely.
However, this is difficult to articulate and extremely hard advice to follow. Perhaps it would be better to put most of your money in an index fund, and do this with the rest of your money long enough to see if it works for you. Sadly, this kind of strategy should be judged over a longer time period (like five years). So, index fund or take your chances.