During the '70s and '80s he was very active with the ensemble Klezmokum, which he founded with Perry Robinson in 1987. Paired with Marion Brown, he plowed down new musical grounds way beyond what jazz was. He had already begun to use prepared electronic tools in Klezmokum even before the computers had started to kick in. In the 80s, it was mostly the sounds of tape and machine and even synthesizers that became an important part of his playing style.
Klezmokum mostly tours India and as the type of music they were playing made a big impact, the whole scene would explode like a bomb. Soon they were also being booked for festivals and TV sessions in Europe. In order to develop these countries' jazz scene, they often invited Greene for concerts and workshops. He would give them a few years after the initial contact, in order to have a deeper impact. In 1997 Tony Brookes, one of Greene's musicians, said: 'Our music was the only thing we liked. We didn't care about what he was doing, we just wanted to hear Woody. We spent two weeks in his flat in Paris. He listened to our CD [Klezmokum] and asked us when we got back to India, 'What is this?' We said: 'It's music. Stop playing that bullshit jazz.' We were so frustrated and he was like, 'OK, school's in session.' We wouldn't let him get away with it! So we said: 'Let's give him a school and see what he can learn.' We took him to the school, and he wanted to play with marimbas. We told him: 'Go ahead.' He played for a year. He learned a couple of things that day. We were right. It wasn't about that. He was trying to do something different.'
In the 90s Greene's mind was the mantra: 'A good jazz musician should be able to do anything, why not go into the jungle. Why not go off into the jungle and then come out with something no one has ever heard before, not even his hat is the same. d2c66b5586