Myocardial perfusion imaging using computed tomography (MPI-CT) and coronary CT angiography (CTA) have the potential to make CT an ideal noninvasive imaging gatekeeper exam for invasive coronary angiography. However, beam hardening can prevent accurate blood flow estimation in dynamic MPI-CT and can create artifacts that resemble flow deficits in single-shot MPI-CT. In this work, we compare four automatic beam hardening correction algorithms (ABHCs) applied to CT images, for their ability to produce accurate single images of contrast and accurate MPI flow maps using images from conventional CT systems, without energy sensitivity. Previously, we reported a method, herein called ABHC-1, where we iteratively optimized a cost function sensitive to beam hardening artifacts in MPI-CT images and used a low order polynomial correction on projections of segmentation-processed CT images. Here, we report results from two new algorithms with higher order polynomial corrections, ABHC-2 and ABHC-3 (with three and seven free parameters, respectively), having potentially better correction but likely reduced estimability. Additionally, we compared results to an algorithm reported by others in the literature (ABHC-NH). Comparisons were made on a digital static phantom with simulated water, bone, and iodine regions; on a digital dynamic anthropomorphic phantom, with simulated blood flow; and on preclinical porcine experiments. We obtained CT images on a prototype spectral detector CT (Philips Healthcare) scanner that provided both conventional and virtual keV images, allowing us to quantitatively compare corrected CT images to virtual keV images. To test these methods' parameter optimization sensitivity to noise, we evaluated results on images obtained using different mAs. In images of the static phantom, ABHC-2 reduced beam hardening artifacts better than our previous ABHC-1 algorithm, giving artifacts smaller than 1.8HU, even in the presence of high noise which should affect parameter optimization. Taken together, the quality of static phantom results ordered ABHC-2>ABHC-3>ABHC-1>>ABHC-NH. In an anthropomorphic MPI-CT simulator with homogeneous myocardial blood flow of 100ml⋅min-1 ⋅100g-1 , blood flow estimation results were 122±24 (FBP), 135±24 (ABHC-NH), 104±14 (ABHC-1), 100±12 (ABHC-2), and 108±18 (ABHC-3) ml⋅min-1 ⋅100g-1 , showing ABHC-2 as a clear winner. Visual and quantitative evaluations showed much improved homogeneity of myocardial flow with ABHC-2, nearly eliminating substantial artifacts in uncorrected flow maps which could be misconstrued as flow deficits. ABHC-2 performed universally better than ABHC-1, ABHC-3, and ABHC-NH in simulations with different acquisitions (varying noise and kVp values). In the presence of a simulated flow deficit, all ABHC methods retained the flow deficit, and ABHC-2 gave the most accurate flow ratio and homogeneity. ABHC-3 corrected phantom flow values were slightly better than ABHC-2, in noiseless images, suggesting that reduced quality in noisy images was due to reduced estimability. In an experiment with a pig expected to have uniform flow, ABHC-2 applied to conventional images improved flow maps to compare favorably to those from 70keV images. The automated algorithm can be used with different parametric BH correction models. ABHC-2 improved MPI-CT blood flow estimation as compared to other approaches and was robust to noisy images. In simulation and preclinical experiments, ABHC-2 gave results approaching gold standard 70keV measurements.