We present improvements to the function representation and generation method used in the Monte Carlo analysis of incomplete ordinary differential equations. Our method widens the scope of the technique to cover cases in which no envelopes have been specified for the function under consideration, thereby extending the applicability of the Monte Carlo approach to the full repertoire of models developed for qualitative reasoning algorithms, and paving the ground for the integrated operation of these two highly complementary techniques. Our new representation does not entail unjustified implicit assumptions about the shape of the generated functions, and provides better coverage of the space of models defined by the input specifications. Our simulator (MOCASSIM) also has the capability of imposing additional restrictions (e.g., convexity) on function shapes, which is particularly useful when the Monte Carlo technique is applied for solving system dynamics problems. (c) 2005 Elsevier Ltd. All rights reserved.