You can set the Maplex Label Engine to be as flexible or rigid in placing labels relative to point features as you need. You can specify a fixed distance that a label will be placed from a feature by defining an offset distance, or you can specify a maximum distance and allow labels to be placed within a range of acceptable distances. If you specify a maximum distance, the label is placed within that range and as close to the offset distance as possible. You can rotate point labels by an angle stored in an attribute of the points or align the labels to the graticules of the data frame. You can also define preferred zones for label placement around the point feature. When setting the values, you can also block a zone from having a label placed in it.