Not so random misfire - need guidance

[squeasel]

Greetings All!,
I have a 2003 X5 3.0. The car misfires in a particular situation, throws code P1347 (Cylinder 3 misfire with fuel-cutoff), but does not throw the SES light (I confirmed this light does work though).

I can recreate the misfire easily enough ... with throttle off (moving or stationary) and RPM around 1,000-ish, a solid push on the throttle causes the misfire to the point where the engine cannot exceed about 1800 RPM for many moments. During the misfire though, if I ease the throttle then go back on the misfire clears.

Same situation ... throttle off RPM about 1000 and a soft push on the throttle causes no issue.

Any thoughts?

Thanks in advance.