We study the cross-section of heavy Higgs production at the LHC within the framework of the constrained MSSM. It is not only enhanced by tan 2β but sometimes is also enhanced by the squark contribution. First, we consider the universal scenario within mSUGRA and find out that to get the desired enhancement one needs large negative values of A0, which seems to be incompatible with the b → sγ decay rate. To improve the situation, we release the unification requirement in the Higgs sector. Then it becomes possible to satisfy all requirements simultaneously and enhance the squark contribution. The latter can gain a factor of several units increasing the overall cross-section which, however, is still smaller than the cross-section of the associated [Formula: see text] production. We consider also some other consequences of the chosen benchmark point.