A series of core-flood tests were performed, together with nuclear magnetic resonance measurements of the initial and residual oil saturation states in the cores, to investigate the recovery and mobilization of bypassed oil using a two-step CO2 soaking and 'huff and puff (huff-n-puff) injection method. Two main factors of interest were focused on: miscibility and size of the bypassed oil. During the initial soaking operation, we found that the ability to remove bypassed oil varies according to the mode used and decreases in the order: first-contact miscibility (FCM), multi-contact (MCM), and immiscibility (IM). The corresponding oil recovery factors are 66.3%, 48.0%, and 28.4%, respectively. FCM also facilitates activation of the bypassed oil to the greatest depth (>= 6 cm), followed by MCM (similar to 3 cm). However, the associated oil recovery factors were found to decrease significantly as the bypassed-oil size was increased from the initial value of 6 cm to 20 cm - where even the FCM mode becomes inefficient. Such size of 6 or 10 cm makes the use of FCM reasonably hopeful (oil recovered: 66.3% and 48.2%, respectively). Smaller ones (6 cm; oil recovery: 48.0%) may be promising for MCM usage (where 3 cm is the best size), but, a size far smaller than 6 cm is needed for IM mode to be effective. Furthermore, in terms of the overall total recovery factor achieved using the two-step soaking and huff-n-puff procedure (bypassed-oil size: 6-20 cm), MCM is the best mode (85.6-86.7%), followed by FCM (69.4-74.0%), and then IM (56.9-59.2%). The size of the bypassed-oil has little effect on the huff-n-puff injection step, which implies this step has a much greater effective activation depth than that of the previous soaking step.