The effect of a number of mechanisms designed to suppress decoherence in open quantum systems are studied with respect to their effectiveness at slowing down the loss of entanglement. The effect of photonic band-gap materials and frequency modulation of the system-bath coupling are along expected lines in this regard. However, other control schemes, like resonance fluorescence, achieve quite the contrary: increasing the strength of the control leads to a faster decay of entanglement. The effect of dynamic decoupling schemes on two qualitatively different system-bath interactions are studied in depth. Dynamic decoupling control has the expected effect of slowing down the decay of entanglement in a two-qubit system coupled to a harmonic oscillator bath under a nondemolition interaction. However, nontrivial phenomena are observed when a Josephson charge qubit, strongly coupled to a random telegraph noise bath, is subject to decoupling pulses. The most striking of these reflects the resonance fluorescence scenario, in that an increase in the pulse strength decreases decoherence but also speeds up the sudden death of entanglement. This demonstrates that the behavior of decoherence and entanglement in time can be qualitatively different in the strong-coupling non-Markovian regime. © 2012 American Physical Society.