Two simplified models of the hardness kernel, eta(r,r') congruent to 1/\r - r'\ and eta(r,r') congruent to delta(r -r'), have been tested to calculate the global hardness for a set of 18 molecules using the hybrid B3LYP functional. It is found that the simplest model, eta(r,r') congruent to delta(r -r'), yields the best ordering of the systems by hardness when compared to experimentally available hardnesses. However, it is worth noting that this approximation provides correct estimates of global hardnesses only after empirical corrections. Finally, it is also shown that the B3LYP method gives results close to conventional ab initio correlated methods.