A multi-leaf collimator is disclosed which alleviates the problems of inter-leaf leakage and pixellation. The collimator comprises a first multi-leaf collimator set, a second multi-leaf collimator set at an acute angle to the first, and a third multi-leaf collimator set at an acute angle to the second. Each multi-leaf collimator set will usually include a pair of leaf banks mutually opposed to each other. The acute angle between the first and the second multi-leaf collimator set is preferably the same as the acute angle between the second and the third set. A suitable angle is about 60.degree.. To improve the penumbra characteristics, (i) the leaves of the multi-leaf collimator closest to the radiation source can be deeper in the direction of the radiation than the leaves of a multi-leaf collimator more distant from the radiation source, (ii) the leaves of the multi-leaf collimator furthest from the radiation source can be shallower in the direction of the radiation than the leaves of a multi-leaf collimator closer to the radiation source, (iii) the tips of the leaves of the multi-leaf collimators can be rounded (iv) the radius of curvature of the tips of the leaves of the multi-leaf collimator closest to the radiation source can be greater than the radius of curvature of the tips of the leaves of a multi-leaf collimator more distant from the radiation source, and (v) the radius of curvature of the tips of the leaves of the multi-leaf collimator furthest from the radiation source can be less than the radius of curvature of the tips of the leaves of a multi-leaf collimator closer to the radiation source. In general, it is also preferred that the first multi-leaf collimator is closest to the radiation source, the third multi-leaf collimator is furthest from the radiation source, and the second multi-leaf collimator is between the first and third multi-leaf collimators.