The computational properties of Synaptic Dynamics (SD) -a type of neuronal plasticity at short timescales- have the potential of enhancing the information processing capabilities of Spiking Neural Networks (SNNs). Models of SD that preserve the biological foundations of synapses can also be beneficial in the field of Computational Neuroscience for studying real synapses. As an example, the Modified Stochastic Synaptic Model (MSSM) is a biophysical model that simulates the SD mechanisms of facilitation and depression. However, we observe an unexpected behaviour of the MSSM under specific conditions when looking at the frequency response of the synaptic efficacy. Further analysis points at unfeasible dynamics of the vesicles and neurotransmitters release, a biologically implausible effect that impacts the fidelity of the MSSM to model the dynamics of SD. Therefore, this paper proposes an adjustment on the equations of the MSSM to correct this unexpected behaviour, which leads to a version of the model with expected frequency responses of synaptic efficacy, balancing and simplifying its equations, and making its dynamics feasible to adequately model SD. The adjustment of the MSSM is not only meant to correctly simulate the mechanisms of facilitation and depression, but also it represents a step forward to equip SNNs with biophysical SD models, enhancing the computational power of such networks with the properties of SD.