In coaxial jet electrosprays inside liquid baths, a conductive liquid forms a cone-jet electrospray within a bath containing a dielectric liquid. An additional dielectric liquid is injected inside the Taylor cone, forming a liquid meniscus. The motion of the conductive liquid that flows toward the vertex cone deforms the inner dielectric meniscus until a liquid jet is issued from its tip. Both the conductive and inner dielectric liquid jets flow coaxially and, further downstream, they will eventually be broken up by capillary instabilities. Coaxial jet electrosprays inside liquid baths is a useful technique to generate fine simple or double emulsions. However, in certain circumstances, we have observed that the dielectric menisci present extremely sharp tips that can be stabilized and made completely steady without mass emission. In this paper, we will first explore the parametrical range of liquid properties, mainly viscosities and surface tensions, under which these sharp tips take place. In addition, a simplified analytical model of the very complex electrohydrodynamical flow is presented for a more complete approach to the phenomena.