What do you mean by randori? Different people use the term differently. For us, randori is multiple attackers, any attack, full speed.
Jiyu waza is a single attacker, any attack, full speed. Some styles refer to this exercise as randori as well.
We have a 7 kyu system (the first test is for 7th kyu -- I used to call it an 8 kyu system 'cause I figured that a person who hasn't tested yet is 8th kyu). We start everyone off on a exercise where we do randori in slow motion -- a slow walking speed -- with special attention paid to giving energy and attacks that really are slowed-down versions of what would happen at full speed. This way, nage gets to really work on body movement, and his ukes learn how to attack and take falls safely. Nages gets two to three times the number of ukes that he'd have to face when going full-speed.
We then also mix in full-speed randori for students who are 5th kyu (or so) and up. Full-speed against two people is required on the 1st kyu test, but our dojo actually does that for 2nd kyu. We do three attackers for 1st kyu. The shodan test, naturally, requires four attackers, and five for nidan, and I think six for sandan.
I've found full-speed training to be very beneficial, but the slow motion training has also helped quite a bit. I just tested for (and was awarded) 3rd kyu this past June. I feel pretty confident that I won't suck when I have to do two-attacker randori for my 2nd kyu test.