In certain communication applications it is advantageous to constrain the shape of the far-field, as to make it act as a spatial filter. This can mitigate interference from other antennas. Such constraints on the far-field behavior, in particular for small antennas tend to increase antenna Q rapidly. To begin to investigate the relation between antenna Q and such far-field bounds, we here consider a case-study with constraint on the partial realized directivity for a two and three parasitic element antenna. The aim is to compare these predictions with a realized parasitic element antenna of the same shape. Note that this paper is a work in progress, and the final comparison between the realized antenna and the fundamental limitations will be discussed at the presentation.