Dual Displays flicker in 3d-mode

I run dual displays (1600x1200x32 bpp, 85Hz on 21" monitors). I am running
Windows XP Professional. I had been using a Geforce4 MX 460, but recently
sold my old system and bought a new one with the FX5800. (I was running dual
displays, and continue to do so.)

I am having a problem with animated objects flickering on the primary
monitor, even though they are on the second monitor, but only in full-screen
games. It is easy to replicate-load a web page with an animation of some
sort in Internet Explorer (or anything) and drag the explorer window to the
2nd display. Next, open up any 3d game I have (Warcraft, Quake III,
Half-Life, etc.) and if the 2nd display updates, it flashes on the first
display for a moment, then vanishes.

When I first started with the fresh copy of XP, it did not do this.. but
started doing it recently. I do not think it has anything to do with any
programs I have installed recently, but I could be wrong. I'm hoping someone
else has had this problem and knows a quick fix.

To reiterate: I am able to replicate the problem with a Geforce4 MX 460,
Geforce FX 5800 in two completely different systems. One was an Athlon 1700+
(Asus A7A Mobo and the other is an Athlon 2100+ (with Nforce2 chipset).