The Gripper is a great tool to use reposition, rotate and scale objects on the fly but did you know you can also reposition The Gripper itself? This can come in really handy because you can snap the gripper origin to any place on the object you want to move and then grab it by the gripper origin and snap it where you want it to go.
For instance say you want to snap the bottom right hand corner of the smaller cube in 6.24.1.tiff to the upper left hand corner of the bigger cube. What you can do is open the Inspector by going to Window-->Inspector. Then click on The Gripper icon and make sure that The Gripper is enabled. Once The Gripper is enabled change the Attach setting from Center of Extents to User Positioned. Then click on the Set Origin Button. Now move your mouse over to the corner of the box you wish to attach it to. When the vertex snap indication appears click to set the Gripper origin. Now select the box and grab The Gripper origin and drag the origin where you want it to go
The Gripper origin will remain here even after you select another object until you set the origin to somewhere else. You can set it back to center of extents at any time and it will always be oriented to the Center of Extents of any selected object when set to that setting.