In this work, we clarified the role of acquisition parameters and quantification methods in myocardial blood flow (MBF) estimability for myocardial perfusion imaging using CT (MPI-CT). We used a physiologic model with a CT simulator to generate time-attenuation curves across a range of imaging conditions, i.e. tube current-time product, imaging duration, and temporal sampling, and physiologic conditions, i.e. MBF and arterial input function width. We assessed MBF estimability by precision (interquartile range of MBF estimates) and bias (difference between median MBF estimate and reference MBF) for multiple quantification methods. Methods included: six existing model-based deconvolution models, such as the plug-flow tissue uptake model (PTU), Fermi function model, and single-compartment model (SCM); two proposed robust physiologic models (RPM1, RPM2); model-independent singular value decomposition with Tikhonov regularization determined by the L-curve criterion (LSVD); and maximum upslope (MUP). Simulations show that MBF estimability is most affected by changes in imaging duration for model-based methods and by changes in tube current-time product and sampling interval for model-independent methods. Models with three parameters, i.e. RPM1, RPM2, and SCM, gave least biased and most precise MBF estimates. The average relative bias (precision) for RPM1, RPM2, and SCM was  ⩽11% (⩽10%) and the models produced high-quality MBF maps in CT simulated phantom data as well as in a porcine model of coronary artery stenosis. In terms of precision, the methods ranked best-to-worst are: RPM1  >  RPM2  >  Fermi  >  SCM  >  LSVD  >  MUP [Formula: see text] other methods. In terms of bias, the models ranked best-to-worst are: SCM  >  RPM2  >  RPM1  >  PTU  >  LSVD [Formula: see text] other methods. Models with four or more parameters, particularly five-parameter models, had very poor precision (as much as 310% uncertainty) and/or significant bias (as much as 493%) and were sensitive to parameter initialization, thus suggesting the presence of multiple local minima. For improved estimates of MBF from MPI-CT, it is recommended to use reduced models that incorporate prior knowledge of physiology and contrast agent uptake, such as the proposed RPM1 and RPM2 models.