I agree with the other answers to this question, but there's a lot to take into consideration. You can be perfectly optimized for the search engines and still never reach the front page of search engine results. If your niche is too competitive, or not specific enough, you can have a very hard time reaching that top 3 ranking... remember EVERYBODY wants to reach that level.
I work with SEO as a copywriter, and most of the mistakes I see is publishing keyword rich content that isn't entirely unique and original. This mistake is being made a lot lately, so it's important to remember that even if something passes copyscape... that doesn't mean it's unique enough to interest a reader.
Beyond the keyword density of optimal keywords, search engines give more priority to websites that are receiving high traffic and low bounce rates.For that reason, your content should be optimized for humans first, and search engines second.
If you're struggling with SEO, I can give you some specific DIY tips on how to improve. Just let me know the niche you are targeting, and what you have done to optimize.