briggidere makes a good suggestion about making another page to optimize for the other search term. However, it's important to write a compelling title that will encourage a user to click on your site. Instead of "Green Widgets", try "Green Widgets at super low prices!". Experiment with different titles, watch your logs, and see what titles are bringing in the most traffic.
Hi, thanks Mona for the advice, I am wondering if adding more words like you suggest would lead to more keyword dilution - that is if keyword dilution exists - that is what I would really like to know.