Suppose you are selling leather date book organizers and you target the word "organizers." There is no way for a searcher to determine if your site has information of interest to someone looking for a "leather organizer" for important papers, a "closet organizer" for a neater home, or a "wedding organizer" to orchestrate that big event. In this case, it is essential that you add a second word to clarify the meaning of "organizer" as it would apply to your site.
Another problem with single word searches is their attainability. Even if a single keyword is what you really want, you may not be able to attain a search engine ranking on it. While it would be nice to be positioned well on a single extremely broad keyword, you might better use your time to pair the keyword with something more specific. More specific keywords have the added advantage of ensuring that your prospects are more qualified. You don't want to disappoint searchers who visit your site in the search of a wedding organizer.
Another example: A search on "software" at almost any search engine will return over a billion documents. The sites at the top of the list are there because of an array of factors, some of which are beyond your control, such as Google's PageRank algorithm that uses link popularity in its rating. It's highly unlikely that your smaller software company could displace Microsoft or another software giant for a first place ranking. Their sites are too popular and have too many links to them to be ousted by a smaller, less well-know software firm. Instead of fighting a losing batter, you should search for a combination term that clearly describes your site and yet returns few enough sites to give you a fighting chance at getting a top ranking.
The bottom line: Don't waste your time fighting for a hard-to-get keyword, unless you're a major player with a powerful brand that dominates your industry. Some keywords will be highly competitive, and you may have to work hard to achieve a top 10 slot. If you find that after all your hard work, you still can't make it into that top 10, just keep working on your other keywords. There are so many other keywords and combinations where your site can achieve a top 10 ranking that you will find that it's not very difficult at all to develop strong traffic from those rankings.
Identify a niche or pocket of keywords that clearly describe your work and that few others are targeting. Then, go after them! Remember, successful SEO requires persistence and perseverance.