Motivated by improved SAT algorithms ((O. Kullmann, DIMACS Series, vol. 35, Amer. Math. Soc., Providence, RI, 1997; O. Kullmann, Theoret. Comput. Sci. (1999); O. Kullmann, Inform. Comput., submitted); yielding new worst-case upper bounds) a natural parameterized generalization GER of Extended Resolution (ER) is introduced. ER can simulate polynomially GER, but GER allows special cases for which exponential lower bounds can be proven. ? 1999 Elsevier Science B.V. All rights reserved.