The excess free energy profile of H2O, O-2, CO, CO2, NO, and CHCl3 has been computed across a fully hydrated dimyristoylphosphatidylcholine (DMPC) bilayer by a cavity insertion variant of the Widom test particle method. This Cavity Insertion Widom (CIW) method modifies the original Widom procedure in such a way that, analogously to the cavity biased particle insertions used in grand canonical and Gibbs ensemble Monte Carlo simulations, it inserts the test particle into cavities of suitable radius only. Results on aqueous systems show that this modification can make the Widom method considerably faster and also more accurate. The free energy profiles obtained are in accordance with the physiological properties of the investigated molecules. It is found that the interior of the membrane constitutes a free energy barrier of about 13 kcal/mol for H2O, and a free energy well of 3-4 kcal/mol for Oz(2) CO, and NO. In contrast to these four free energy profiles, which change monotonically between the two phases of the membrane, the free energy profile of CO2 has about 4 kcal/mol deep wells in the two interfacial regions. While, due to its larger size, the results for CHCl3 are considerably less accurate than for the other five solutes it could still be concluded that its excess free energy is a few kilocalories per mole lower in the interior of the membrane than in the aqueous phase, and the headgroup regions constitute large free energy barriers.