In my current series of articles following the lifetime of a Drip, we are now looking at the characteristics that define prospective investments. Generally speaking, we look for strong growth companies with an impressive future.

This made me wonder, when charting a company's price versus time, what price curve (or performance) would be best when purchasing regularly through a Drip? The optimum curve is going to differ from what one would like to see with an outright purchase.

When I make an outright purchase (buying a full investment stake at once), the best-case scenario is that the price chart looks like a steep, rising hill. I hold the stock, the price moves up. I hold longer, the price moves up more. The longer I hold, the more it moves up. It doesn't get any better than that.

But, is this the best-case scenario when you invest through Drips? I don't think so.

Remember that we are committing ourselves to numerous purchases over a long period of time. That being the case, the faster the price moves up, the more expensive our purchases become. An elevated share price too early in our investing lifetimes will actually work against our eventual goal.

What's the answer? What type of price/time curve will work best for Drippers? The obvious wrong answer would be an incredible run-up in the stock price during the first year of a 10-year timeline, then a flattened curve during the remaining nine years. Although this investment makes you happy initially, the majority of the purchases are made at the high point, and years later you won't be so happy.

One might think that the perfect curve would be one where the stock is absolutely flat for the first nine years, then makes its entire move during the last year. In a way, this is the optimal answer, because nearly all of the purchases are made at a time when the stock's price is the lowest in that scenario.

However, it takes guts of steel for one to continue purchasing a company that is stagnant year after year, expecting it to make a very incredible run at the very end of its timeline. Remember, for that to be successful, the stock would need to make up a lot of ground very quickly. This can rarely be done in such a small period of time as one year.

Perfect, then, would be a hyperbolic curve. In this case, the price remains relatively stagnant for the first few years, followed by several years of moderate gains, completed with the last few years of incredible growth. You can look at a 10-year chart of Enron (NYSE: ENE) to see what I mean.

Does this mean that we should be looking for companies with initial flat growth? I can just imagine the cries of protest! I would be one of the protesters! The problem is that it is impossible to look so far into the future and find evidence of eventual, impressive growth after years of slower growth. Talk about the ultimate in long-term market timing!

So, is trying to aim for slower growth first followed by faster growth later just a wacky idea, or is there some practicality to it? If you have thoughts on this, join us on the Drip Companies discussion board (and tell us which companies you think fit the bill, if you think there's merit to the idea). It will be interesting to see if there are any out-of-the-box investing concepts related to this out there in the Fool community.