  Considering pure quantum states, entanglement concentration is the procedure
where from $N$ copies of a partially entangled state, a single state with
higher entanglement can be obtained. Getting a maximally entangled state is
possible for $N=1$. However, the associated success probability can be
extremely low while increasing the system's dimensionality. In this work, we
study two methods to achieve a probabilistic entanglement concentration for
bipartite quantum systems with a large dimensionality for $N=1$, regarding a
reasonably good probability of success at the expense of having a non-maximal
entanglement. Firstly, we define an efficiency function $\mathcal{Q}$
considering a tradeoff between the amount of entanglement (quantified by the
I-Concurrence) of the final state after the concentration procedure and its
success probability, which leads to solving a quadratic optimization problem.
We found an analytical solution, ensuring that an optimal scheme for
entanglement concentration can always be found in terms of $\mathcal{Q}$.
Finally, a second method was explored, which is based on fixing the success
probability and searching for the maximum amount of entanglement attainable.
Both ways resemble the Procrustean method applied to a subset of the most
significant Schmidt coefficients but obtaining non-maximally entangled states.
