Actually the 5D MKII can do very well with longer exposures, up to 50 minutes in my experience.
I leave the long exposure noise reduction set to "on" not auto. These exposures were for star trail
work.
The 5D MKII will take a dark frame the same length of time as the original frame. net 50 minute exposure, then a dark frame for 50 minutes.
Make sure you have a fully charged battery, I have the grip which allows the use of 2. You don't have to wait the full 50 minutes to shoot again
as the camera will be available to shoot within 30 sec to 1 minute. However you have to wait until the red light is off before you turn it off.
From my everyday use, the 5D MKII up to 10 minutes is as clean as any camera I have used only the new Nikon D3s (very impressive) seems
better. Past 10 minutes, you will start to see a good bit of noise, but as Doug mentioned, the latest version of Capture One 5.x will take the vast
majority of this noise out. The noise will look very bad on the LCD, but don't let that worry you, until you open the file in a raw converter, make
sure you use raw also.
Lightroom 2.x does not seem to work as well on these really long exposures, I have not tried the beta 3.x yet.
In you question, you mentioned 1 minute to a couple of minutes, from my experience, you should not have any problems
with a 5D MKII here, noise will be very low as long as you stay at ISO 50 or 100.
Paul Caldwell