Stochastic programming with step decision rules, SPSDR, is an attempt to overcome the curse of computational complexity of multistage stochastic programming problems. SPSDR combines several techniques. The first idea is to work with independent experts. Each expert is confronted with a sample of scenarios drawn at random from the original stochastic process. The second idea is to have each expert work with step decision rules. The optimal decision rules of the individual experts are then averaged to form the final decision rule. The final solution is tested on a very large sample of scenarios. SPSDR is then tested against two alternative methods: regular stochastic programming on a problem with 3 stages and 2 recourses; robust optimization with affinely adjustable recourses on a 12-stage model. The performance of the new method turns out to be competitive on those examples, while it permits a tighter control on computational complexity than standard stochastic programming.