This paper studies labour market policy in a society where differently gifted individuals can invest in training to further increase their labour market productivity. Furthermore, the government seeks both efficiency and equity. Frictions in the matching process create unemployment and differently skilled workers face different unemployment risks. We show that in such an environment, training programmes targeted to the disadvantaged workers complement passive transfers (UI benefits), unlike a general training subsidy. Combining passive subsidies with a training subsidy conditioned on individual unemployment duration – the typical Active Labour Market Programme – implies a favorable trade-off between equity and efficiency which encourages relative high spending on training.