I've never heard of Kuk's method, but the hot topic these days is L1 minimisation. The rationale being that if you use a penalty term of the absolute value of the regression coefficients, the unimportant ones should go to zero.
These techniques have some funny names: Lasso, LARS, Dantzig selector. You can read the papers, but a good place to start is with Elements of Statistical LearningElements of Statistical Learning, Chapter 3.