Is this an absolutely terrible idea?

Having just fitted laminate to two rooms I noticed how much of the job
entails ripping up the old carpet, underlay, gripper rods, then cleaning
and fitting fiberboard underlay for the laminate. I am using the
floormaster glueless variety.

About to start the third room when an idea occurs to me. There is
reasonably decent carpet down. Could I use this as the underlay and
simply put the laminate over it? It is a first floor room - so
damp-proof membrane not required. I can also easily cope with the
additional floor height this would involve.

Is this feasible or completely crazy?

--
Matthew Barnard