Buying and selling stocks in increments is rational
It turns out that Apple, Inc.'s stock (ticker: AAPL) was a stellar performer in 2007. It also performed really well in 2006:

Perhaps surprisingly, the purpose of this entry isn't to pump AAPL. Instead I'm going to explain how buying and selling stocks in increments is one of the most powerful money-making (and money-preserving) tools you can utilize as a stock investor.
Increments? I want BIG gains!
What do I mean by "buying and selling stocks in increments?" Have a seat on my hypothetical stock sofa. Ask yourself, "What is my stock investing dream?" If you're like me, it involves something along the lines of: buy 1,000,000 shares low and sell 1,000,000 shares high. I'm a king! Hooray... hooray... feed me grapes, dammit ... HOORAY! er... ah hem.
Let me clarify; that used to be something like my stock dream.
Reality kicked in and I learned the hard way that I'm not very good at predicting what will happen to a stock price tomorrow or next week or even a month from now. Ultimately I figured out that when I do thorough homework on a company/stock, my odds of making profit over the long term are a lot better. Over the short term, forget about it.
Given that tomorrow my favorite stock could trade at a discount compared to how it's trading today, why not snap up that bargain tomorrow? Then again, it could sky-rocket on a buy-out rumor, too. Face it: without [probably illegal] insider trading information, you never really know what's going to happen to a stock price in the future.
Accept it, learn it, live it. Come up with trading strategies that embrace this philosophy. Don't worry; I'm not going Plato on you, but check out the following scenarios that illustrate the advantages of buying in increments. Small pieces... not big chunks.
Let's assume you have $300k to "play" with (ha!).
Example 1: The quickly skyrocketing stock
Suppose you buy 1,000 shares of a stock that's trading for $85 / share. Within a few weeks the stock is trading around $98 / share. Sweet!You sell all and catch a net gain of $13k or 15%. Yeah, you could have bought 3,500 shares and made a bunch more money... but you just made $13k in a few weeks! If you're sad about making $13k in a few weeks, you may have other problems.
Example 2: The tanking stock
Suppose you buy 4,000 shares of a stock that's trading for $75 / share. You're sure that conditions haven't changed, but the stock drops immediately after your purchase. The next month it hits $60 / share. The next month it hits $50 / share.Ouch. Now you're down $100k or 33%. If only you had the power to see the future and had waited those two months... or realistically, what if you had purchased 1,000 shares at $75 / share. You'd still be down 33%, but that 33% would translate into a loss of a more manageable $25k instead $100k. I don't know about you, but if I absolutely had to choose between losing $25k or $100k then first I'd click my heels together three times and then I'd pick the $25k loss.
Example 3: The tanking stock that recovers
You buy another 1,250 shares at $60 / share; same total cost of $75k, but this time you get more shares. Good deal! You've spent $150k so far and have another $150k in cash.
A month passes and the "impossible" happens: your stock sinks to $50 / share. You're nervous, angry, and you've begun to consume your daily share of Top-Ramen noodles... but you're confident that your research and evaluation of economic conditions are spot on. This time $75k buys you 1,500 shares. You somehow remain calm. You're left with $75k in cash and you've spent $225k purchasing stock.
Incredibly positive news comes out and within a month your stock shoots back up toward $75/share. Nice! If you had invested all your $300k @ $75 / share initially, you'd be breaking even and back to $300k.
Since instead you invested wisely and broke your purchase into three increments, your 3,750 shares are now worth $281k for a 25% gain. Add that to your $75k cash and your portfolio has grown from $300k to $356k ($281k stock + $75k cash). Again, you could have broken even but instead you're up $50k+. Winner!
Conclusion
As you can see, buying in increments has its definite advantages while the disadvantages are few. Yeah, yeah ... in Example 1 you could have made more money, but let's not be greedy. Profit is profit is profit.
In a future entry I'll go through some examples to illustrate how selling in increments can also be very advantageous. Sure, there are some situations where experts advise dumping all (for example when there's an abrupt executive management change), but even in those cases you never know beforehand if it's the most profitable thing to do.
In general if you sell in increments you can lock in gains while also giving your stock the chance to climb higher (while also shielding yourself from potentially more severe losses). Craziness, a free lunch, the best of both worlds, and so on. Woohoo!
If you can tell the future, disregard everything I've written in this entry today. If you're like me and can't tell the future (go Packers!), consider buying stock in increments instead of in one big chunk (this process is also known as dollar cost averaging). You just might thank yourself later.
Oh, by the way... all the above three examples track AAPL stock movement over some period in the last two years. Check it out:

Full disclosure: I do not have any position, long or short, in AAPL at the time of writing.
The more I "play" in the market, the more your strategy makes sense. There's just one thing that's preventing me from getting "more" of something I already own, once it's at a bargain: diversification. If you have $300k, you can diversify pretty easily. But if you have more like $30k, it's a little harder. (Don't even get me started on $3k ;-) I've found that what I really want to do is buy the "first increment" of a lot of different things before I go back and add to what I've got based on whether I think they're still something good to buy.
Good points, Dave (as always!).
I don't know the perfect solution to that diversification quandary, but I have some ideas. One would be to slap a portion of excess cash into a market tracking exchange-traded fund (ETF) or perhaps even an ETF that's designed to track the weak area your portfolio. Even in those cases I'd recommend moving only portions of money at a time vs. an entire position. People should be careful, though, because if one blindly purchases securities for the purposes of diversification then one could end up with as dire a situation as not being diversified. Cash in a money market account is usually worth more than the value of a sinking stock/ETF/fund, after all.
I'd argue, even, that cash in a money market account can provide some level of diversification. I can reason that it all goes back to controlling what you can control: your actions, not the price of securities.
That's tough to do especially with "small" account balances, where for some reason it's incredibly tempting to buy something... ANYTHING ... whenever there's cash lying around. Although somewhat counter intuitive, maintaining a cash reserve can provide a means to maximize gains. In other words, although it may seem like you are short-changing yourself by maintaining a non-trivial cash position you can actually use it to your advantage depending on the movement of the stock(s). Buy a little low, sell a little high. Buy low, buy lower, sell on the way up, sell even higher.
Buying/selling in that manner seems easier when you have more money to work with, especially considering most brokerages charge trading commissions. *shrug*
Going back to your idea about buying a "first increment" of several things before adding to a position isn't a bad idea at all. It definitely serves to reduce portfolio risk. A lot of this stuff comes down to risk, and different people are comfortable with all different levels of risk.