[Walt Fricke]

Good advice, Ed. You are reporting misbehavior in a specified engine RPM range. The CIS system doesn't know, in a sense, what your RPMs are. It knows closed throttle, part throttle, and wide open throttle. It also knows (if this is a US car) what your air/fuel ratio is, and tries to optimize that. You don't say if the problem varies with how much throttle you give it, but I assume this happens no matter how hard you are trying to accelerate? But it likely isn't an injector or fuel pump issue, as those would not show up just in a fairly narrow range. This is more like the flat spots you sometimes find with carburetors. And from your description the engine starts and idles fine, and runs fine above 4,000 RPM.

Having a shop check out the CIS to see if it is in spec, and the distributor to see if the advance is working correctly would be a good idea.