Multi-post-labeling-delay pseudo-continuous arterial spin labeling (multi-PLD PCASL) allows for absolute quantification of the cerebral blood flow (CBF) as well as the arterial transit time (ATT). Estimating these perfusion parameters from multi-PLD PCASL data is a non-linear inverse problem, which is commonly tackled by fitting the single-compartment model (SCM) for PCASL, with CBF and ATT as free parameters. The longitudinal relaxation time of tissue T1t is an important parameter in this model, as it governs the decay of the perfusion signal entirely upon entry in the imaging voxel. Conventionally, T1t is fixed to a population average. This approach can cause CBF quantification errors, as T1t can vary significantly inter- and intra-subject. This study compares the impact on CBF quantification, in terms of accuracy and precision, of either fixing T1t, the conventional approach, or estimating it alongside CBF and ATT. It is shown that the conventional approach can cause a significant bias in CBF. Indeed, simulation experiments reveal that if T1t is fixed to a value that is 10% off its true value, this may already result in a bias of 15% in CBF. On the other hand, as is shown by both simulation and real data experiments, estimating T1t along with CBF and ATT results in a loss of CBF precision of the same order, even if the experiment design is optimized for the latter estimation problem. Simulation experiments suggest that an optimal balance between accuracy and precision of CBF estimation from multi-PLD PCASL data can be expected when using the two-parameter estimator with a fixed T1t value between population averages of T1t and the longitudinal relaxation time of blood T1b.@en