A gas turbine engine has a fan rotor, a first compressor rotor and a second compressor rotor. The second compressor rotor compresses air to a higher pressure than the first compressor rotor. A first turbine rotor drives the second compressor rotor and a second turbine rotor. The second turbine drives the compressor rotor. A fan drive turbine is positioned downstream of the second turbine rotor. The fan drive turbine drives the fan through a gear reduction. The first compressor rotor and second turbine rotor rotate as an intermediate speed spool. The second compressor rotor and first turbine rotor together as a high speed spool. The high speed spool and the fan drive turbine configured to rotate in the same first direction. The intermediate speed spool rotates in an opposed, second direction.