  Quantum mechanics dictates bounds for the minimal evolution time between
predetermined initial and final states. Several of these Quantum Speed Limit
(QSL) bounds were derived for non-unitary dynamics using different approaches.
Here, we perform a systematic analysis of the most common QSL bounds in the
damped Jaynes-Cummings model, covering the Markovian and non-Markovian regime.
We show that only one of the analysed bounds cleaves to the essence of the QSL
theory outlined in the pioneer works of Mandelstam \& Tamm and Margolus \&
Levitin in the context of unitary evolutions. We also show that all of QSL
bounds analysed reflect the fact that in our model non-Markovian effects speed
up the quantum evolution. However, it is not possible to infer the Markovian or
non-Markovian behaviour of the dynamics only analysing the QSL bounds.
