Someone posted the video link below in a thread about how to grip a pistol. It also demonstrates point shooting the 1911 pistol. Notice how they say the closer to eye level you bring the pistol, the more accurate you will be. Hip firing,
in my opinion, should only be done closer in.
Combat Firing with Hand Guns (1944)
At ranges of 3-7 yards I can usually score center mass hits focusing on the target, if I bring my pistol close to eye level. The lower the pistol is in my plane of vision the larger my grouping becomes. With a 1911 type pistol I use my regular two, or one handed hold and I have found focusing on the head, puts my shots in the torso.
For pocket pistols I really like the technique called
The Zipper. Which is where you begin firing as soon as the pistol comes parallel to the target and you continue to fire as you bring the pistol up to eye level. All the while your focus is on the target.