Using the Graph Editor for Key Frame Efficiency

I have started looking at the timing of my 'struck' animation now that I have almost completed the pose-to-pose for it. I noticed that when I remove frames between two keys that the staff and hand controller aren't moving quite as quick as everything else, and so the result is the staff detaching from the hand's grip as shown in the image below:

Hand and staff moving apart. The graph showing slow-dipping arc path.

Here you can also see why the controller is behaving this way in the graph editor. To correct this error you can either insert a new key frame between the two where the error is occurring where you want the staff to be, which will correct it but also increase the amount of frames you have and therefore decrease the efficiency of your animation, or you can do what I chose to do and manipulate the key frames' values by breaking and freeing their tangents, and moving them so that in this case the Translate-Z value is brought down in a quick space of time, which will make the staff move in the Z axis more quickly and therefore allow the hand and staff to stay as an unbroken link.

The hand and staff are now together again. The graph is showing a sharper decline from the first to the second frame in context.