If you’re a heavy iPhone user who also owns a PC, you’ve probably experienced the annoyance of having to get up from a comfy couch or an office meeting to go back from your phone to your computer for something.

For 99 cents, Splashtop’s new iPhone app, Remote Desktop, lets you fire up your computer’s display on the iPhone. You can control apps, click and type at them, even play audio and video from your computer over the iPhone.

Remote Desktop runs on newer iPhones—the 3GS and 4 versions—as well as on the third and fourth-generation iPod Touch.

Splashtop builds the instant-boot systems that ship with many PCs — Lenovo Quick Start, Asus ExpressGate, HP QuickWeb — so it’s no surprise that Remote Desktop is small, fast and reliable. And cheap. The company says its goal is to become a widely used go-anywhere platform, rather than to make money selling apps, so they’ve knocked the price down from an original $7 for the iPad to just $1 for the new iPhone app.

To connect your iPhone to a computer, both need to be on the same Wi-Fi network. That can be at home, at an office, or in a hotel room. Install the Splashtop app on your iPhone and another small, free download on your computer. It’ll work on Windows XP, Vista and Windows 7 computers, and there’s a beta version for Mac OS X 10.6.

You’ll be prompted to create a password for remote access. After that, the iPhone app will find your computer when you start it up. (My own PC always resets its Windows theme and resolution when I first connect, but the company said that seemed to be a bug that didn’t bite most users. I reset my theme to my favorite Windows 7 Aero configuration, and it worked just fine.)

I reviewed and praised Splashtop’s iPad version of the app a few weeks ago, but I was suspicious that it would be as breezy to use on a smaller phone screen. I was both right and wrong. On new iPhones and iPods with Apple’s high-resolution Retina Display, it’s surprising how easy it is to see and read an entire PC desktop on the phone’s screen. But trying to mouse-click on Outlook by finger-tapping on the iPhone was frustrating.

To make it easier, Splashtop has added two controls not available on their iPad version. First, you can enlarge the remote screen image by pinching and stretching it on the iPhone, as with a Web page. Second, you can skip trying to grab tiny scrollbars with one fingertip and instead swipe up or down with two fingers to scroll a window on the computer.

What can you do with Remote Desktop that you can’t do on the iPhone itself? For starters, it’ll let you play Flash and other videos that the iPhone doesn’t support. It’ll also let you play the music stored on your PC or Mac without needing to sync it to the iPhone first. And it’s also good for checking Outlook, Office, or other apps for information without needing to find and configure a corresponding iPhone app.

Unlike the iPad version, Remote Desktop doesn’t run smoothly in real time on an iPhone. There’s a definite lag between the time you tap and the time the screen responds. On a wimpy netbook, that delay stretched up to ten seconds. On a more powerful PC or iMac, my delays were usually a fraction of a second.

Also, it helps to spend a few minutes training yourself to position the remote cursor accurately with your fingertip. Otherwise you’ll find yourself clicking the wrong buttons and links, which coupled with the delayed response can be frustrating.

To practice, sit in front of your computer screen with your iPhone running Splashtop. As you tap around, you’ll see immediately on the computer screen exactly where you’ve positioned its cursor. A few minutes with this sort of feedback made me a lot better at driving around with one finger. Right now I’m watching The Big Lebowski from my PC’s iTunes library while lounging in my favorite backyard chair, a glass in one hand and an iPod Touch in the other. I’m sure The Dude would approve.