We introduce a computational method for classifying Lie algebras admitting a nilsoliton inner product in a large subclass of the set of all nilpotent Lie algebras. This method does not rely on any preexisting classifications of nilpotent Lie algebras. The subclass consists of all nilpotent Lie algebras whose associated Nikolayevsky derivation D-N has distinct positive eigenvalues and so that the Gram matrix associated to D-N is nonsingular. We use our method to classify the nilpotent Lie algebras in this class in dimensions 7 and 8 that admit nilsoliton inner products, and we present all such nilsoliton metric Lie algebras. We also classify the nilpotent Lie algebras that do not admit a nilsoliton inner product in the class in dimensions 7 and 8. (C) 2012 Elsevier B.V. All rights reserved.