Films of vertically aligned carbon nanotubes (CNTs) have recently being grown within patterned areas. Nanotriodes based on such CNT arrays as field emitters have the potential of improved performance if devising a way to subject the nanotubes to uniform extraction fields. In this paper, we propose and model an optimized nanotriode with CNTs of variable heights. The bunch of variable-height CNTs is centrally placed in the opening of the gate electrode, the CNTs being taller in the middle and shorter toward the bunch edge. An analytical model to describe the electric field distribution is derived. The nanotriode characteristics have been calculated as function of the device geometry and its functional parameters. Optimal nanotriode configurations assuring quasi-uniform extraction fields and enhanced emission currents have been shown to exist.