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We demonstrate that the performance of students in an introductory Physics course, a major stumbling block for Engineers, may be improved by a homework regime involving complex, multiple step problems. In introductory courses the work done out of class, or "homework" represents the principal method of training students in the manipulation of class material. In a standard Introductory Physics course for Engineers the homework problems are typically short, and involve a single application of a single concept; we have demonstrated that this encourages memorization of formulae. We have examined whether the use of complex multiple step homework problems might improve student performance. A group of "complex" homework problems were devised for an Introductory Physics course. Student performance was measured on standard tests where a number of the problems had an extensive past history with which we could compare. We also assess changes in performance by using the technique of Discriminant Analysis which predicts student performance on the basis of historical records. Training with the "complex" problems raised student performance of the whole class by about half a letter grade and reduced the proportion of unsatisfactory grades by one hag The improvement is principally among those students who we would have predicted to attain a C in thecourse and occurs at the final examination rather than on periodic tests. Thus the use of "complex" problems for training purposes enhances the long term pegormanee of students who we would normally expect to attain lower levels of grades. We suggest that the problems provided by standard texts do not provide the optimum mechanism for training students and that they should be supplemented by "complex" problems involving multiple manipulations.