Muon catalyzed fusion of deuterium and tritium (muCF) yields the same energy gain per reaction as fusion with magnetic or inertial confinement (17.6 MeV). The crucial points of muCf are, however, very different, namely (a) the energy cost W(mu) for production of one mu- and (b) the number n of reactions a single muon can catalyze on the average. (b) is ultimately limited by the effective sticking probability omega(f) : n less-than-or-equal-to 1/omega(f). With ''standard'' methods one has W(mu) almost-equal-to 5 GeV, omega(f) = 0.5%. Hence a ''standard'' muCF reactor can never reach a net energy gain. To solve this problem, ways discussed since about a decade are to increase the efficiency by both (i) energy multiplication using a fissionable blanket and (ii) breeding. A new way to increase the safety of fission devices mostly due to Yu. Petrov is outlined. On the other hand there is a hope to lower W(mu) slightly and omega(f) drastically, the latter by artificial reactivation. New theoretical results for beam cooling in an omegatron type driven integrated muCF reactor, important for W(mu) and, in particular, omega(f), is presented.