Apple (AAPL 0.16%) gave fans of its smaller phones something to cheer about earlier this year, releasing the new 4-inch iPhone SE. In addition to being smaller than Apple's flagship phones, the iPhone SE is also its cheapest iPhone ever, with a starting price of just $399 in the U.S.

That low price has some analysts concerned that the iPhone SE is cannibalizing sales of more expensive phones from the iPhone 6 product line. However, these fears may be overstated, as many consumers have strong preferences about smartphone size.

Some analysts fear that the iPhone SE is cannibalizing iPhone 6-series sales. Image source: Apple.

The iPhone SE gets off to a solid start

Since going on sale at the end of March, the iPhone SE has claimed a respectable slice of total iPhone sales. According to research firm Consumer Intelligence Research Partners, the iPhone SE accounted for 16% of Apple's iPhone sales in the U.S. last quarter. That was still well behind the sales shares of the iPhone 6s (39%) and iPhone 6s Plus (26%), though.

CIRP noted that the combined domestic sales share of the iPhone 6s and iPhone 6s Plus (65%) is well below the 82% domestic sales share achieved by the iPhone 6 and iPhone 6 Plus in the year-earlier quarter. Thus, Apple probably faced an unfavorable shift in the iPhone sales mix last quarter, with a higher proportion of buyers opting for cheaper models.

Is the iPhone SE stealing sales from pricier phones?

It's not necessarily good for Apple that the iPhone SE is selling well. That depends on how much the iPhone SE is cannibalizing sales of high-end models like the iPhone 6s versus expanding the market. As CIRP co-founder Josh Lowitz stated:

On the one hand, the SE may have persuaded these owners of older iPhones to upgrade to a new phone, and possibly remain with Apple iOS. On the other hand, with its much lower retail price, iPhone SE also may have diverted these customers from purchasing a more-expensive iPhone 6/6S series phone, which will likely lead to a lower ASP in the quarter.

Fortunately for Apple, the former reason appears to have been more prevalent. A lot of iPhone users who prefer smaller phones had been holding out for a new 4-inch model, and the iPhone SE spurred them to upgrade.

This can be seen from the surprisingly large proportion of iPhone SE buyers who were upgrading from very old iPhones. A third of iPhone SE buyers upgraded from pre-iPhone 5 models -- primarily the iPhone 4 and iPhone 4S -- according to CIRP. (Another third of iPhone SE buyers came from somewhat newer iPhone 5-series phones.)

Many iPhone SE buyers had held onto their old iPhones for a long time. Image source: Apple.

Clearly, most of these users have had plenty of opportunities to upgrade before. Had Apple not released a new 4-inch iPhone, they may have held onto their aging phones indefinitely -- or even abandoned the iOS ecosystem entirely.

Some people want small smartphones

Obviously, there has been some cannibalization of the iPhone 6 and iPhone 6s by the iPhone SE. Many users have a strong preference either for larger phones or smaller phones, but there's also a middle ground of people who would have been happy with a more expensive iPhone but instead bought an iPhone SE because it was available.

Nevertheless, there was clearly a large pool of pent-up demand for smaller phones ahead of the iPhone SE launch earlier this year. After the initial rush of iPhone fans desperate for bigger phones in late 2014 and 2015, iPhone sales have started to slow.

Yet there are still hundreds of millions of people around the world using pre-iPhone 6 devices. Back in January, Apple CEO Tim Cook stated that only 40% of iPhone users had upgraded to the larger iPhone 6 and 6s-series models. What have these customers been waiting for -- if not a new 4-inch design?

Thus, the launch of this new 4-inch iPhone model could spur millions of incremental upgrades over the next year. That should easily outweigh the impact of some customers trading down from pricier models.